A295772 a(n) = Sum_{k=0..n} binomial((n-k)*k, k).

1, 1, 2, 4, 11, 41, 189, 1020, 6277, 43262, 328963, 2727076, 24425913, 234743744, 2406904525, 26202132494, 301579542517, 3656552470482, 46555182556971, 620695577790512, 8644238847922949, 125472134647552497, 1894393648378487895, 29696659293381522674

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..508

Formula

log(a(n)) ~ n*(log(n) - log(log(n)) + (log(log(n)) - 1)/log(n)). - Vaclav Kotesovec, Jan 10 2023

Maple

seq(add(binomial((n-k)*k, k), k=0..n), n=0..30); # Robert Israel, Nov 27 2017

Mathematica

Table[Sum[Binomial[(n-k)*k, k], {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A060539, A226391, A264409.

Sequence in context: A013182 A013170 A094762 * A099934 A067353 A105996

Adjacent sequences: A295769 A295770 A295771 * A295773 A295774 A295775

Keyword

nonn,easy

Author

Vaclav Kotesovec, Nov 27 2017

Status

approved