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 A198513 E.g.f.: Sum_{n>=0} sinh(n*x)^n/n!. 1

%I

%S 1,1,4,28,320,5556,129600,3756936,132872192,5679982288,286769980416,

%T 16732506817280,1115928688967680,84383735744758464,

%U 7163164003950936064,676619301019539271040,70674282825174467215360,8117559039240651749888256

%N E.g.f.: Sum_{n>=0} sinh(n*x)^n/n!.

%F E.g.f.: Sum_{n>=0} exp(-n^2*x) * (exp(2*n*x) - 1)^n / (2^n*n!).

%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 28*x^3/3! + 320*x^4/4! + 5556*x^5/5! +...

%e where

%e A(x) = 1 + sinh(x) + sinh(2*x)^2/2! + sinh(3*x)^3/3! + sinh(4*x)^4/4! +...

%o (PARI) {a(n)=local(A=sum(m=0,n,sinh(m*x+x*O(x^n))^m/m!));n!*polcoeff(A,n)}

%Y Cf. A108459.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 26 2011

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