A328088 a(n) = Sum_{k=4..n} ( binomial(n,k)*(k-2)*(2^k-2*k-2) ) - (2^n-n-1).

1, 94, 683, 3520, 15461, 61826, 232543, 838276, 2930585, 10014406, 33633299, 111448904, 365403853, 1187875594, 3834883271, 12309375244, 39320806145, 125090127950, 396537120379, 1253145232336, 3949433330741, 12416933938834, 38953666980143, 121962851990420, 381179210953321, 1189376848680406, 3705576521235683

Offset: 4

Author

N. J. A. Sloane, Oct 17 2019

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 4..2087
• J. B. Remmel et al., The combinatorial properties of the Benoumhani polynomials for the Whitney numbers of Dowling lattices, Discrete Math., 342 (2019), 2966-2983. See page 2981, formula for coefficient of m in B_{m+1}(n,n-2).
• Index entries for linear recurrences with constant coefficients, signature (14,-82,260,-481,518,-300,72).

Crossrefs

For the constant term see A000460.

Programs

Maple

f:= n -> 3^(n-1)*(2*n-6) + 2^(n-1)*(-n^2+n+6) - n - 1:
map(f, [$4..40]); # Robert Israel, Oct 18 2019

PARI

Vec(x^4*(1 + 80*x - 551*x^2 + 1406*x^3 - 1772*x^4 + 1128*x^5 - 288*x^6) / ((1 - x)^2*(1 - 2*x)^3*(1 - 3*x)^2) + O(x^40)) \\ Colin Barker, Oct 19 2019

Formula

a(n) = 3^(n-1)*(2*n-6) + 2^(n-1)*(-n^2+n+6) - n - 1. - Robert Israel, Oct 18 2019

From Colin Barker, Oct 19 2019: (Start)

G.f.: x^4*(1 + 80*x - 551*x^2 + 1406*x^3 - 1772*x^4 + 1128*x^5 - 288*x^6) / ((1 - x)^2*(1 - 2*x)^3*(1 - 3*x)^2).

a(n) = -1 + 3*2^n - 2*3^n + (1/6)*(-6 + 3*2^n + 4*3^n)*n - 2^(-1+n)*n^2 for n>3.

a(n) = 14*a(n-1) - 82*a(n-2) + 260*a(n-3) - 481*a(n-4) + 518*a(n-5) - 300*a(n-6) + 72*a(n-7) for n>10.

(End)

E.g.f.: x^2/2 + 2*x^3/3 + exp(2*x)*(3 - 2*x^2 + (-3 + x)*cosh(x) + (-1 + 3*x)*sinh(x)). - Stefano Spezia, Oct 19 2019