A094938 a(n)=(-36^n/18)*B(2n,1/6)/B(2n,1/3) where B(n,x) is the n-th Bernoulli polynomial.

1, 63, 2511, 92583, 3352671, 120873303, 4353033231, 156723545223, 5642176768191, 203119525916343, 7312313393341551, 263243376303474663, 9476762394213697311, 341163453817290588183, 12281884406052838539471

Offset: 1

Author

Benoit Cloitre, Jun 19 2004

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (45,-324).

Crossrefs

Cf. A096054.

Programs

Mathematica

LinearRecurrence[{45,-324},{1,63},20] (* Harvey P. Dale, Mar 09 2018 *)

PARI

B(n,x)=sum(i=0,n,binomial(n,i)*bernfrac(i)*x^(n-i));a(n)=(-36^n/18)*B(n,1/6)/B(n,1/3)

Formula

a(n)=9^n/18*(4^n-2)

a(n)=9^(n-1)/2*(2^(2n)-2) - Harvey P. Dale, Mar 09 2018

G.f.: x*(1+18*x) / ( (36*x-1)*(9*x-1) ). - R. J. Mathar, Nov 15 2019

Extensions

Incorrect recurrence formula deleted by Harvey P. Dale, Mar 09 2018