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E.g.f.: Sum_{n>=0} (n^2)^n * cosh(n^2*x) * x^n/n!.
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%I #3 Oct 27 2012 19:20:07

%S 1,1,16,732,67072,10356120,2428502016,806564304896,360766703665152,

%T 209198209220565120,152649491877210357760,136856491451984089032192,

%U 147838797016098042267303936,189330891572377497747235278848,283553443348816020717858371665920

%N E.g.f.: Sum_{n>=0} (n^2)^n * cosh(n^2*x) * x^n/n!.

%C Compare e.g.f. to the o.g.f. of A007820: Sum_{n>=0} (n^2)^n * exp(-n^2*x) * x^n/n!.

%e E.g.f.: A(x) = 1 + x + 16*x^2/2! + 732*x^3/3! + 67072*x^4/4! + 10356120*x^5/5! +...

%o (PARI) {a(n)=polcoeff(serlaplace(sum(k=0,n,(k^2*x)^k/k!*cosh(-k^2*x +x*O(x^n)))),n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A007820.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 27 2012