A339032 Expansion of (4*x^5 - 9*x^4 + 17*x^3 - 15*x^2 + 6*x - 1)/((2*x - 1)^2*(x - 1)^3).

1, 1, 3, 10, 31, 86, 219, 526, 1215, 2734, 6043, 13190, 28527, 61270, 130875, 278302, 589567, 1244894, 2621115, 5504662, 11533935, 24116806, 50331163, 104857070, 218103231, 452984206, 939523419, 1946156326, 4026531055, 8321498294, 17179868283, 35433479230

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).

Formula

a(n) = ((n + 2)*2^n - 2*n^2 - 2)/2 for n >= 1. - Charles R Greathouse IV, May 31 2026

Maple

gf := (4*x^5 - 9*x^4 + 17*x^3 - 15*x^2 + 6*x - 1)/((2*x - 1)^2*(x - 1)^3):
ser := series(gf, x, 33): seq(coeff(ser, x, n), n=0..31);

Mathematica

CoefficientList[Series[(4x^5-9x^4+17x^3-15x^2+6x-1)/((2x-1)^2(x-1)^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{7, -19, 25, -16, 4}, {1, 1, 3, 10, 31, 86}, 40] (* Harvey P. Dale, Jan 28 2026 *)

Prog

(PARI) a(n)=if(n, (n+2)*2^n/2-n^2-1, 1) \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Row sums of A339031.

Cf. A339030.

Sequence in context: A360563 A290061 A212031 * A374925 A033121 A180432

Adjacent sequences: A339029 A339030 A339031 * A339033 A339034 A339035

Keyword

nonn,easy

Author

Peter Luschny, Nov 24 2020

Status

approved