Offsets of tables
Leroy Quet
qq-quet at mindspring.com
Sun Jun 26 22:07:32 CEST 2005
I just submitted the sequence below, which is an array read off by
diagonals.
But the purpose of this post is not the sequence itself, but is to ask
how a sequence's offset should be submitted when the sequence is from a 2
(or more) dimensional table and the offsets for different indexes are not
necessarily the same.
(In my example, n starts at 0, m starts at 1.)
thanks,
Leroy Quet
>%S A000001 1,1,1,1,3,2,1,5,11,6,1,7,26,50,24
>%N A000001 a(m,n) = m!*H(n,m), where H(n,m) is a higher order harmonic
>number.
>(H(0,m) = 1/m. H(n,m) = sum{k=1 to m} H(n-1,k).)
>%C A000001 In array m index runs from 1 on, n index runs from 0 on.
>%F A000001 a(m,n) = (H_{m+n-1}-H_{n-1})(m+n-1)!/(n-1)!,
>where H_k = H(1,k), a standard harmonic number.
>Array is read off by diagonals.
>%e A000001 a(2,3) = (1 + (1 +1/2) + (1 +1/2 +1/3))*6 = 26.
>%Y A000001 A000254
>%O A000001 0
>%K A000001 ,easy,more,nonn,tabl,
>%A A000001 Leroy Quet (qq-quet at mindspring.com), Jun 26 2005
>RH
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