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

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

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)

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}]

Prog

(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

Crossrefs

Cf. A001117.

Sequence in context: A223815 A275414 A223309 * A346108 A271879 A016676

Adjacent sequences: A179480 A179481 A179482 * A179484 A179485 A179486

Keyword

sign,easy

Author

M. Lawrence Glasser, Jul 16 2010

Status

approved