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Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.
3

%I #11 Oct 08 2022 08:33:15

%S 0,1,4,20,160,1872,25024,348224,5055488,78571776,1332573184,

%T 24695206912,493816963072,10492449771520,234399640633344,

%U 5480635606908928,134015043318054912,3427700843478056960,91642829715498336256,2556218693498006929408

%N Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.

%F a(n) = Sum_{k=0..floor((n-1)/2)} 4^(n-1-k) * Stirling2(n,2*k+1).

%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/2)/2)))

%o (PARI) a(n) = sum(k=0, (n-1)\2, 4^(n-1-k)*stirling(n, 2*k+1, 2));

%Y Cf. A024429, A357664, A357665.

%Y Cf. A357598, A357617, A357663.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 07 2022