A083014 a(n) = Sum_{k=0..n-1} 10^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number.

0, 1, -9, 36, 81, -1524, -4779, 155316, 643761, -28041444, -145069299, 7794224196, 48371836041, -3078058903764, -22284938832219, 1637087002046676, 13545357290061921, -1127884947406124484, -10498665795419017539, 977073296798704710756

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..417

Ira M. Gessel, On the Almkvist-Meurman Theorem for Bernoulli Polynomials, Integers (2023) Vol. 23, #A14.

Formula

E.g.f.: 10*x/(Sum_{i=0..9} exp(i*x)). - Alois P. Heinz, Sep 28 2016

Mathematica

Range[0, 15]! CoefficientList[ Series[ 10x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x] + Exp[ 5x] + Exp[ 6x] + Exp[ 7x] + Exp[ 8x] + Exp[ 9x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)
Array[Sum[10^k*BernoulliB[k]*Binomial[#, k], {k, 0, # - 1}] &, 20, 0] (* Michael De Vlieger, Feb 14 2023 *)

Prog

(PARI) a(n)=sum(k=0, n-1, 10^k*binomial(n, k)*bernfrac(k))

Crossrefs

Cf. A001469.

Cf. A036968, A083007, A083008, A083009, A083010, A083011, A083012, A083013.

Sequence in context: A016766 A242538 A083353 * A202287 A001487 A175673

Adjacent sequences: A083011 A083012 A083013 * A083015 A083016 A083017

Keyword

sign

Author

Benoit Cloitre, May 31 2003

Extensions

Offset changed to 0 by Seiichi Manyama, Sep 28 2016

Status

approved