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

%I #10 Oct 08 2022 08:33:11

%S 0,1,3,12,81,765,7938,85239,963819,11801862,158533443,2320621569,

%T 36425289816,604576791405,10532817901791,192197187209484,

%U 3673078679995677,73486862051182425,1536507360834633666,33482575797899354235,758209049155176114807

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

%F a(n) = Sum_{k=0..floor((n-1)/2)} 3^(n-1-k) * Stirling2(n,2*k+1).

%o (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 (PARI) a(n) = sum(k=0, (n-1)\2, 3^(n-1-k)*stirling(n, 2*k+1, 2));

%Y Cf. A024429, A357664, A357666.

%Y Cf. A356572, A357572, A357662.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 07 2022