A179483 A(k,3) where A(k,n) = Sum_{m=1..k} (-1)^(m+1) *binomial(n,m)*m^k.

3, -9, 6, 36, 150, 540, 1806, 5796, 18150, 55980, 171006, 519156, 1569750, 4733820, 14250606, 42850116, 128746950, 386634060, 1160688606, 3483638676, 10454061750, 31368476700, 94118013006, 282379204836, 847187946150, 2541664501740, 7625194831806

Offset: 1

Author

M. Lawrence Glasser, Jul 16 2010

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A001117.

Programs

Maple

A179483 := proc(n) add( (-1)^(m+1)*binomial(3,m)*m^n,m=1..n) ; end proc: # R. J. Mathar, Jan 31 2011

Mathematica

Sum[(-1)^(m+1)Binomial[3,m]m^k,{m,1,k}]

PARI

Vec(3*x*(1 - 9*x + 31*x^2 - 39*x^3 + 18*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, May 21 2017

Formula

a(n) = A001117(n), n>=3. - R. J. Mathar, Jul 20 2010

From Colin Barker, May 21 2017: (Start)

G.f.: 3*x*(1 - 9*x + 31*x^2 - 39*x^3 + 18*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

a(n) = 3 - 3*2^n + 3^n for n>2.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>5.

(End)