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L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^4 + 1) ).
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%I #5 Sep 08 2015 18:16:51

%S 2,30,1300,115380,18362616,4800297144,1929066361136,1131386990471376,

%T 929148154976860592,1033280101490424757200,1513696127276317671503232,

%U 2854591502346208585710465024,6796099969466204436648991894784,20087194984043555807709161038217856,72648127998052140755125407470469776640

%N L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^4 + 1) ).

%e L.g.f.: L(x) = 2*x + 30*x^2/2 + 1300*x^3/3 + 115380*x^4/4 + 18362616*x^5/5 + 4800297144*x^6/6 +...

%e where

%e exp(L(x)) = 1 + 2*x + 34*x^2/2! + 2788*x^3/3! + 716516*x^4/4! + 448539016*x^5/5! + 581755103752*x^6/6! +...+ A255434(n)*x^n/n! +...

%o (PARI) {a(n) = n*polcoeff( log(sum(m=0,n+1,x^m/m!*prod(k=1,m,k^4+1)) +x*O(x^n)), n)}

%o for(n=1,30,print1(a(n),", "))

%Y Cf. A255434.

%K nonn

%O 1,1

%A _Paul D. Hanna_, Sep 08 2015