A262005 - OEIS

%I #8 Sep 09 2015 12:36:16

%S 2,62,7862,2727962,2142727322,3338786909702,9359997562264862,

%T 43832263835648182562,323596944389808203151362,

%U 3595937015557095119026724222,57916971628198473192636867273302,1310203094399724255301396007844469562,40540285568379172649032878682803332843162,1677228560345389865386245848706087738381702662

%N L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^5 + 1) ).

%F a(n) == 2 (mod 60) for n>=1 (conjecture).

%e L.g.f.: L(x) = 2*x + 62*x^2/2 + 7862*x^3/3 + 2727962*x^4/4 + 2142727322*x^5/5 + 3338786909702*x^6/6 +...

%e such that

%e exp(L(x)) = 1 + 2*x + 33*x^2 + 2684*x^3 + 687775*x^4 + 429996930*x^5 + 557347687435*x^6 +...+ x^n/n!*Product_{k=1..n} (k^5 + 1) +...

%o (PARI) {a(n) = n*polcoeff( log(sum(m=0, n+1, x^m/m!*prod(k=1, m, k^5+1)) +x*O(x^n)), n)}

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

%K nonn

%O 1,1

%A _Paul D. Hanna_, Sep 08 2015