%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