A272358 a(n) = n*(945*n^4 - 3150*n^3 + 4095*n^2 - 2370*n + 496).

0, 16, 4112, 65208, 387424, 1439480, 4068096, 9611392, 20012288, 37931904, 66862960, 111243176, 176568672, 269507368, 398012384, 571435440, 800640256, 1098115952, 1478090448, 1956643864, 2551821920, 3283749336, 4174743232, 5249426528, 6534841344, 8060562400

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 (6,-15,20,-15,6,-1).

Formula

O.g.f.: 8*x*(2 + 502*x + 5097*x^2 + 7192*x^3 + 1382*x^4)/(1-x)^6.

E.g.f.: x*(16 + 2040*x + 8820*x^2 + 6300*x^3 + 945*x^4)*exp(x).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), for n>5.

a(n) = 2*n^2*A272357(n) - n*(2*n-1)*A272357(n-1), see page 7 in Brent's paper.

Mathematica

Table[n (945 n^4 - 3150 n^3 + 4095 n^2 - 2370 n + 496), {n, 0, 40}]

Prog

(Magma) [n*(945*n^4 - 3150*n^3 + 4095*n^2 - 2370*n + 496): n in [0..40]];
(PARI) a(n)=n*(945*n^4-3150*n^3+4095*n^2-2370*n+496) \\ Charles R Greathouse IV, Apr 28 2016

Crossrefs

Cf. A272357.

Sequence in context: A193134 A139296 A268757 * A176369 A090045 A201241

Adjacent sequences: A272355 A272356 A272357 * A272359 A272360 A272361

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 27 2016

Status

approved