A096054 a(n) = (36^n/6)*B(2n,1/6)/B(2n) where B(n,x) is the n-th Bernoulli polynomial and B(k) = B(k,0) is the k-th Bernoulli number.

1, 91, 3751, 138811, 5028751, 181308931, 6529545751, 235085301451, 8463265086751, 304679288612371, 10968470088963751, 394865064451017691, 14215143591303768751, 511745180725868773411, 18422826609078989373751, 663221758853362301815531, 23875983327059668074930751

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (50,-553,1800,-1296).

Formula

a(n) = (1/12)*(36^n - 2*9^n - 3*4^n+6).

From Colin Barker, May 30 2020: (Start)

G.f.: x*(1 - 6*x)*(1 + 47*x + 36*x^2) / ((1 - x)*(1 - 4*x)*(1 - 9*x)*(1 - 36*x)).

a(n) = 50*a(n-1) - 553*a(n-2) + 1800*a(n-3) - 1296*a(n-4) for n>4. (End)

Mathematica

a[n_] := 6^(2*n-1) * BernoulliB[2*n, 1/6] / BernoulliB[2*n]; Array[a, 15] (* Amiram Eldar, May 07 2025 *)
LinearRecurrence[{50, -553, 1800, -1296}, {1, 91, 3751, 138811}, 20] (* Harvey P. Dale, May 15 2026 *)

Prog

(PARI) a(n)=(1/12)*36^n-(1/6)*9^n-(1/4)*4^n+1/2;

Crossrefs

Cf. A083420, A096045, A096046, A096047, A096048, A096053.

Sequence in context: A169937 A378965 A047697 * A129965 A017807 A017754

Adjacent sequences: A096051 A096052 A096053 * A096055 A096056 A096057

Keyword

nonn,easy

Author

Benoit Cloitre, Jun 18 2004

Status

approved