A274311 a(n) = 15*binomial(n,6)-6*binomial(n-2,4)+binomial(n-4,4).

0, 0, 9, 75, 331, 1055, 2745, 6209, 12670, 23886, 42285, 71115, 114609, 178165, 268541, 394065, 564860, 793084, 1093185, 1482171, 1979895, 2609355, 3397009, 4373105, 5572026, 7032650, 8798725, 10919259, 13448925, 16448481, 19985205, 24133345, 28974584, 34598520, 41103161, 48595435, 57191715

Offset

4,3

Links

Colin Barker, Table of n, a(n) for n = 4..1000

Q. T. Bach, R. Paudyal, J. B. Remmel, A Fibonacci analogue of Stirling numbers, arXiv preprint arXiv:1510.04310 [math.CO], 2015. (Note that a(15) is given incorrectly in the first arXiv version)

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

From Colin Barker, Jun 24 2016: (Start)

a(n) = (240+452*n-220*n^2-101*n^3+75*n^4-15*n^5+n^6)/48 for n>3.

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7) for n>8.

G.f.: x^6*(9+12*x-5*x^2-2*x^3+x^4) / (1-x)^7.

(End)

Maple

f:=n->15*binomial(n, 6)-6*binomial(n-2, 4)+binomial(n-4, 4);
[seq(f(n), n=4..50)];

Mathematica

Table[15 Binomial[n, 6] - 6 Binomial[n - 2, 4] + Binomial[n - 4, 4], {n, 4, 40}] (* Vincenzo Librandi, Jun 25 2016 *)

Prog

(PARI) concat([0, 0], Vec(x^6*(9+12*x-5*x^2-2*x^3+x^4)/(1-x)^7 + O(x^40))) \\ Colin Barker, Jun 24 2016
(Magma) [15*Binomial(n, 6)-6*Binomial(n-2, 4)+Binomial(n-4, 4): n in [4..40]]; // Vincenzo Librandi, Jun 25 2016

Crossrefs

Sequence in context: A102094 A321234 A339483 * A281804 A210045 A125397

Adjacent sequences: A274308 A274309 A274310 * A274312 A274313 A274314

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 24 2016

Status

approved