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

Author

Paul Barry, Mar 28 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A018678, A027649, A081674.

Programs

Magma

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

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)