A262003 L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^3 + 1) ).

2, 14, 206, 4754, 156722, 7002926, 408890414, 30315895970, 2787655430690, 311698491417614, 41677029833666702, 6569530958412341810, 1205946558621750623186, 255076631360949322977710, 61594259272103652501480686, 16842210623928858086134293314, 5177422625829616613400965034818, 1777829320507196831744636014160654

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Formula

Logarithmic derivative of A262011.

Example

 L.g.f.: L(x) = 2*x + 14*x^2/2 + 206*x^3/3 + 4754*x^4/4 + 156722*x^5/5 + 7002926*x^6/6 +...
where
exp(L(x)) = 1 + 2*x + 9*x^2 + 84*x^3 + 1365*x^4 + 34398*x^5 + 1244061*x^6 +...+ A262011(n)*x^n +...

Prog

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

Crossrefs

Cf. A262011.

Sequence in context: A054652 A122647 A158097 * A271847 A136550 A068369

Adjacent sequences: A262000 A262001 A262002 * A262004 A262005 A262006

Keyword

nonn

Author

Paul D. Hanna, Sep 08 2015

Status

approved