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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

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).

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}]}]

Prog

(PARI) a(n) = sum(k=0, n, (k*(k+1)/2)^n); \\ Michel Marcus, Aug 24 2023

Crossrefs

Cf. A000217, A031971, A177385.

Sequence in context: A122836 A116878 A218307 * A034222 A197437 A268545

Adjacent sequences: A249561 A249562 A249563 * A249565 A249566 A249567

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 01 2014

Extensions

New name from Peter Bala, Aug 18 2023

Status

approved