This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A295772 #16 Nov 13 2024 12:22:00
%S A295772 1,1,2,4,11,41,189,1020,6277,43262,328963,2727076,24425913,234743744,
%T A295772 2406904525,26202132494,301579542517,3656552470482,46555182556971,
%U A295772 620695577790512,8644238847922949,125472134647552497,1894393648378487895,29696659293381522674
%N A295772 a(n) = Sum_{k=0..n} binomial((n-k)*k, k).
%H A295772 Robert Israel, <a href="/A295772/b295772.txt">Table of n, a(n) for n = 0..508</a>
%F A295772 log(a(n)) ~ n*(log(n) - log(log(n)) + (log(log(n)) - 1)/log(n)). - _Vaclav Kotesovec_, Jan 10 2023
%F A295772 G.f. A(x) = 1 + x*Sum_{n>=0} x^n/n! * ( d^n/dy^n (1+y)^n/(1 - x*(1+y)^n) ) evaluated at y = 0. - _Paul D. Hanna_, Nov 13 2024
%e A295772 G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 11*x^4 + 41*x^5 + 189*x^6 + 1020*x^7 + 6277*x^8 + 43262*x^9 + 328963*x^10 + ...
%p A295772 seq(add(binomial((n-k)*k,k),k=0..n),n=0..30); # _Robert Israel_, Nov 27 2017
%t A295772 Table[Sum[Binomial[(n-k)*k, k], {k, 0, n}], {n, 0, 30}]
%Y A295772 Cf. A060539, A226391, A264409.
%K A295772 nonn,easy
%O A295772 0,3
%A A295772 _Vaclav Kotesovec_, Nov 27 2017