A295772 - OEIS

%I #12 Jul 28 2023 21:17:12

%S 1,1,2,4,11,41,189,1020,6277,43262,328963,2727076,24425913,234743744,

%T 2406904525,26202132494,301579542517,3656552470482,46555182556971,

%U 620695577790512,8644238847922949,125472134647552497,1894393648378487895,29696659293381522674

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

%H Robert Israel, <a href="/A295772/b295772.txt">Table of n, a(n) for n = 0..508</a>

%F log(a(n)) ~ n*(log(n) - log(log(n)) + (log(log(n)) - 1)/log(n)). - _Vaclav Kotesovec_, Jan 10 2023

%p seq(add(binomial((n-k)*k,k),k=0..n),n=0..30); # _Robert Israel_, Nov 27 2017

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

%Y Cf. A060539, A226391, A264409.

%K nonn,easy

%O 0,3

%A _Vaclav Kotesovec_, Nov 27 2017