A038165 G.f.: 1/((1-x)*(1-x^2))^5.

1, 5, 20, 60, 160, 376, 820, 1660, 3190, 5830, 10252, 17380, 28600, 45760, 71500, 109252, 163735, 240955, 348920, 497640, 700128, 972400, 1334840, 1812200, 2435420, 3241628, 4276520, 5594360, 7261040, 9354080, 11966504, 15206840

Offset

0,2

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (5, -5, -15, 35, 1, -65, 45, 45, -65, 1, 35, -15, -5, 5, -1).

Formula

a(2*k) = binomial(k + 7, 7)*(4*k^2 + 23*k + 18)/18 = A059601(k); a(2*k + 1) = binomial(k + 7, 7)*(4*k^2 + 41*k + 90)/18 = A059602(k), k >= 0.

G.f.: 1/(1 - 5*x + 5*x^2 + 15*x^3 - 35*x^4 - x^5 + 65*x^6 - 45*x^7 - 45*x^8 + 65*x^9 - x^10 - 35*x^11 + 15*x^12 + 5*x^13 - 5*x^14 + x^15). - Charles R Greathouse IV, May 19 2026

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2))^5, {x, 0, 35}], x]  (* Harvey P. Dale, Apr 02 2011 *)

Prog

(PARI) Vec(1/((1+x)^5*(1-x)^10)+O(x^99)) \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A008619, A006918, A038163.

Sequence in context: A256540 A319888 A319869 * A327383 A339588 A344099

Adjacent sequences: A038162 A038163 A038164 * A038166 A038167 A038168

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved