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 A357665 #10 Oct 08 2022 08:33:11 %S A357665 0,1,3,12,81,765,7938,85239,963819,11801862,158533443,2320621569, %T A357665 36425289816,604576791405,10532817901791,192197187209484, %U A357665 3673078679995677,73486862051182425,1536507360834633666,33482575797899354235,758209049155176114807 %N A357665 Expansion of e.g.f. sinh( (exp(3*x) - 1)/sqrt(3) )/sqrt(3). %F A357665 a(n) = Sum_{k=0..floor((n-1)/2)} 3^(n-1-k) * Stirling2(n,2*k+1). %o A357665 (PARI) my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(3*x)-1)/sqrt(3))/sqrt(3))))) %o A357665 (PARI) a(n) = sum(k=0, (n-1)\2, 3^(n-1-k)*stirling(n, 2*k+1, 2)); %Y A357665 Cf. A024429, A357664, A357666. %Y A357665 Cf. A356572, A357572, A357662. %K A357665 nonn %O A357665 0,3 %A A357665 _Seiichi Manyama_, Oct 07 2022