A272357 a(n) = n*(105*n^3 - 210*n^2 + 147*n - 34).

0, 8, 520, 4056, 15656, 42880, 95808, 187040, 331696, 547416, 854360, 1275208, 1835160, 2561936, 3485776, 4639440, 6058208, 7779880, 9844776, 12295736, 15178120, 18539808, 22431200, 26905216, 32017296, 37825400, 44390008, 51774120, 60043256, 69265456

Offset

0,2

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.: 8*x*(1 + 60*x + 192*x^2 + 62*x^3)/(1-x)^5.

E.g.f.: x*(8 + 252*x + 420*x^2 + 105*x^3)*exp(x).

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

See page 7 in Brent's paper:

a(n) = 2*n^2*A272134(n) - n*(2*n - 1)*A272134(n-1),

A272358(n) = 2*n^2*a(n) - n*(2*n - 1)*a(n-1).

Mathematica

Table[n (105 n^3 - 210 n^2 + 147 n - 34), {n, 0, 40}]

Prog

(Magma) [n*(105*n^3-210*n^2+147*n-34): n in [0..40]];
(PARI) concat(0, Vec(8*x*(1+60*x+192*x^2+62*x^3)/(1-x)^5 + O(x^99))) \\ Altug Alkan, Jul 06 2016

Crossrefs

Cf. A272134, A272358.

Sequence in context: A015480 A159532 A003397 * A241367 A121740 A216353

Adjacent sequences: A272354 A272355 A272356 * A272358 A272359 A272360

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 27 2016

Status

approved