A249564 a(n) = Sum_{k = 0..n} (k*(k+1)/2)^n.
1, 1, 10, 244, 11378, 867395, 98204132, 15475158552, 3239399341956, 869652788703285, 291315412833808702, 119114020598815073524, 58386684085633233147478, 33797341113242898165287495, 22810507257314647778044971848, 17755122836243141585656207243952
Offset: 0
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..200
Programs
-
Mathematica
Table[n!*SeriesCoefficient[Sum[Exp[x*k*(k+1)/2], {k, 0, n}], {x, 0, n}], {n, 0, 20}] Flatten[{1,Table[Sum[(k*(k+1)/2)^n,{k,1,n}],{n,1,20}]}] -
PARI
a(n) = sum(k=0, n, (k*(k+1)/2)^n); \\ Michel Marcus, Aug 24 2023
Formula
E.g.f.: Sum_{n>=0} exp(x*n*(n+1)/2).
a(n) ~ exp(3) * n^(2*n) / ((exp(2)-1) * 2^n).
Extensions
New name from Peter Bala, Aug 18 2023