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 A294395 #16 Nov 01 2024 04:25:07
%S A294395 1,1,3,67,289,5121,71731,861043,18134817,303946849,6724342531,
%T A294395 146426154051,3533373668353,93259190078497,2489644674735219,
%U A294395 75193364720030131,2265438714279130561,74716734198386887233,2543592184722884351107,90853513680763023292099
%N A294395 E.g.f.: exp(Sum_{n>=1} A050999(n) * x^n).
%H A294395 Seiichi Manyama, <a href="/A294395/b294395.txt">Table of n, a(n) for n = 0..422</a>
%F A294395 a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*A050999(k)*a(n-k)/(n-k)! for n > 0.
%F A294395 a(n) ~ (3*zeta(3))^(1/8) * n^(n - 1/8) / (2*exp(n - 4*zeta(3)^(1/4) * n^(3/4) / 3^(3/4) - n^(1/4) / (4*3^(5/4)*zeta(3)^(1/4)))). - _Vaclav Kotesovec_, Nov 01 2024
%o A294395 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, d^2*(d%2))*x^k))))
%Y A294395 E.g.f.: exp(Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): A294392 (k=0), A294394 (k=1), this sequence (k=2).
%Y A294395 Cf. A050999, A262811.
%K A294395 nonn
%O A294395 0,3
%A A294395 _Seiichi Manyama_, Oct 30 2017