[seqfan] Re: puzzled by central binomials in A094796
Don Reble
djr at nk.ca
Sat Nov 16 00:25:03 CET 2019
> I don't understand A094796.
> %S 1,3,1,9,15,6,27,108,135,42,81,594,1539,1530,456,243,2835,12555,25245,
> %T 22122,6120,729,12393,83835,281475,482436,383292,101520
> %C Let D_0(n)=binomial(2*n,n) and
> D_{k+1}(n)=D_{k}(n+1)-D_{k}(n),
> then D_{k}(n)=binomial(2*n,n)*(n+1)*(n+2)*...*(n+k)*P_{k}(n)
> where P_{k} is a polynomial with integer coefficients of degree k.
It should be
"then D_{k}(n)*(n+1)*(n+2)*...*(n+k) = binomial(2*n,n)*P_{k}(n)"
We might as well do the %U line.
%S A094796 1,3,1,9,15,6,27,108,135,42,81,594,1539,1530,456,243,2835,12555,
%T A094796 25245,22122,6120,729,12393,83835,281475,482436,383292,101520,
%U A094796 2187,51030,489888,2466450,6916833,10546200,7786692,1980720
--
Don Reble djr at nk.ca
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