cp's OEIS Frontend

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.

A357665 Expansion of e.g.f. sinh( (exp(3*x) - 1)/sqrt(3) )/sqrt(3).

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%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