A262005 L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^5 + 1) ).

2, 62, 7862, 2727962, 2142727322, 3338786909702, 9359997562264862, 43832263835648182562, 323596944389808203151362, 3595937015557095119026724222, 57916971628198473192636867273302, 1310203094399724255301396007844469562, 40540285568379172649032878682803332843162, 1677228560345389865386245848706087738381702662

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

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 +...
such that
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) +...

Prog

(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)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A239786 A209183 A200802 * A296278 A239744 A024238

Adjacent sequences: A262002 A262003 A262004 * A262006 A262007 A262008

Keyword

nonn

Author

Paul D. Hanna, Sep 08 2015

Status

approved