[seqfan] row sums of triangles

N. J. A. Sloane njas at research.att.com
Fri May 29 00:50:34 CEST 2009

Dear Seqfans, This message is from Emeric Deutsch and me:

It would be nice if the row-sum sequence for each triangle
in the OEIS was also in the OEIS.

Picking an example at random, we see this triangle:

%I A156740
%S A156740 1,1,1,1,153,1,1,4845,4845,1,1,74613,2362745,74613,1,1,735471,358664691,
%T A156740 358664691,735471,1,1,5311735,25533510145,393216056233,25533510145,
%U A156740 5311735,1,1,30421755,1056158828725,160324910200455,160324910200455
%N A156740 A higher order odd Narayana-Roirdan triangle sequence:i=7; q-factorial odd product: f(n)= Product[2*k - 1, {k, 0, n}]; Narayana combinations: a(n,m)-=Binomial[n, m]*f[n]/(f[m]*f[n - m]); General product form: t[n,m,i] = Product[a(n + k, m + k)/a(n - m + k, k), {k, 0, i}]
%C A156740 Row sums are:
%C A156740 {1, 2, 155, 9692, 2511973, 718800326, 444293699995, 322762198901872,
%C A156740 375936459278442977, 517934214393739253282, 977731835276897269439162,...}.
%F A156740 i=7;
%F A156740 q-factorial odd product:
%e A156740 {1},
%e A156740 {1, 1},
%e A156740 {1, 153, 1},
%e A156740 {1, 4845, 4845, 1},
%e A156740 {1, 74613, 2362745, 74613, 1},
%K A156740 nonn,tabl,uned
%O A156740 0,5
%A A156740 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 14 2009

with keyword "tabl" (the same applies to keyword "tabf").

Here we are told the row-sum sequence, yet it is not in the OEIS.

So we add it, as follows (use your name as the author, for simplicity):

%I A151614
%S A151614 1,2,155,9692,2511973,718800326,444293699995,322762198901872,
%T A151614 375936459278442977,517934214393739253282,977731835276897269439162
%N A151614 Row sums of A156740.
%O A151614 0,2
%K A151614 nonn
%A A151614 N. J. A. Sloane (njas(AT)research.att.com), May 28 2009

We use the same offset as in the original.  (This has keyword "uned", but 
that's fine for the moment.)

We also add a cross-reference line to the original entry:

%Y A156740 Row sums are in A151614.

We would like to encourage everyone to pick a bunch of triangles 
and do the same thing!  Of course many row-sum sequences
are already in the OEIS, although they may not be identified as such
(if they aren't, send in a cross-reference)


Emeric Deutsch
Neil Sloane

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