A272132 a(n) = 6144*n^4 - 29184*n^3 + 52416*n^2 - 41840*n + 12465.

12465, 1, 3281, 68385, 388849, 1305665, 3307281, 7029601, 13255985, 22917249, 37091665, 57004961, 84030321, 119688385, 165647249, 223722465, 295877041, 384221441, 491013585, 618658849, 769710065, 946867521, 1152978961, 1391039585, 1664192049, 1975726465

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014 (page 16).

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

O.g.f.: (12465 - 62324*x + 127926*x^2 - 72660*x^3 + 142049*x^4)/(1-x)^5.

E.g.f.: (12465 - 12464*x + 7872*x^2 + 7680*x^3 + 6144*x^4)*exp(x).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

See page 7 in Brent's paper:

a(n) = (2*n-1)^2*A272131(n) - 4*(n-1)^2*A272131(n-1).

A272133(n) = (2*n-1)^2*a(n) - 4*(n-1)^2*a(n-1).

n*a(n) = 1 + 3^9*(n-1)/(n+1) + 5^9*((n-1)*(n-2))/((n+1)*(n+2)) + ... for n >= 1. See A245244. - Peter Bala, Jan 19 2019

Maple

[6144*n^4-29184*n^3+52416*n^2-41840*n+12465$n=0..30]; # Muniru A Asiru, Jan 28 2019

Mathematica

Table[6144 n^4 - 29184 n^3 + 52416 n^2 - 41840 n + 12465, {n, 0, 40}]
LinearRecurrence[{5, -10, 10, -5, 1}, {12465, 1, 3281, 68385, 388849}, 30] (* Harvey P. Dale, Aug 06 2022 *)

Prog

(Magma) [6144*n^4 - 29184*n^3 + 52416*n^2 - 41840*n + 12465: n in [0..40]];
(PARI) lista(nn) = for(n=0, nn, print1(6144*n^4-29184*n^3+52416*n^2-41840*n+12465, ", ")); \\ Altug Alkan, Apr 26 2016

Crossrefs

Cf. A272131, A272133, A245244.

Sequence in context: A221016 A237901 A234127 * A206664 A033669 A203345

Adjacent sequences: A272129 A272130 A272131 * A272133 A272134 A272135

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 26 2016

Status

approved