login
Expansion of e.g.f. cosh( (exp(2*x) - 1)/sqrt(2) ).
3

%I #13 Oct 08 2022 08:32:58

%S 1,0,2,12,60,320,2040,15568,133648,1230336,11962400,123144384,

%T 1349008320,15731096576,194349866880,2527082917120,34392647418112,

%U 488243791183872,7216792525799936,110936087161801728,1771199461131500544,29324602146652307456

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

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

%o (PARI) my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cosh((exp(2*x)-1)/sqrt(2)))))

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

%Y Cf. A024430, A357662, A357663.

%Y Cf. A009153, A264036, A357664.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 07 2022