A081675 Generalized Poly-Bernoulli numbers.

0, 1, 8, 50, 286, 1566, 8358, 43870, 227606, 1170926, 5985958, 30454590, 154371126, 780246286, 3934789958, 19808175710, 99577765846, 500036345646, 2508771728358, 12578218511230, 63028531771766, 315692415197006, 1580661100289158, 7912101596565150, 39595692359108886

Offset

0,3

Comments

Binomial transform of A081674. Second binomial transform of A027649.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-38,40).

Formula

a(n) = (4*5^n - 3*4^n - 2^n)/6.

G.f.: x*(1-3*x)/((1-2*x)*(1-4*x)*(1-5*x)).

From Elmo R. Oliveira, Aug 29 2024: (Start)

E.g.f.: exp(2*x)*(4*exp(3*x) - 3*exp(2*x) - 1)/6.

a(n) = 11*a(n-1) - 38*a(n-2) + 40*a(n-3) for n > 2. (End)

Prog

(Magma) [(4*5^n-3*4^n-2^n)/6: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011

Crossrefs

Cf. A018678, A027649, A081674.

Sequence in context: A033463 A030279 A133357 * A283277 A081180 A052177

Adjacent sequences: A081672 A081673 A081674 * A081676 A081677 A081678

Keyword

easy,nonn

Author

Paul Barry, Mar 28 2003

Status

approved