A290071 a(n) = (1/48)*n*(n+5)^2*(1*n^3 + 7*n^2 + 16*n + 28).

0, 39, 196, 664, 1809, 4250, 8954, 17346, 31434, 53949, 88500, 139744, 213571, 317304, 459914, 652250, 907284, 1240371, 1669524, 2215704, 2903125, 3759574, 4816746, 6110594, 7681694, 9575625, 11843364, 14541696, 17733639, 21488884, 25884250, 31004154, 36941096

Offset: 0

Author

Gregory Gerard Wojnar, Jul 19 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

This is the negation of column 4 in triangle A290053.

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,39,196,664,1809,4250,8954},40] (* Harvey P. Dale, Nov 15 2022 *)

PARI

concat(0, Vec(x*(39 - 77*x + 111*x^2 - 88*x^3 + 36*x^4 - 6*x^5) / (1 - x)^7 + O(x^50))) \\ Colin Barker, Jul 20 2017

PARI

vector(50,n,n*(n+5)^2*(n^3+7*n^2+16*n+28)/48) \\ Derek Orr, Jul 24 2017

Formula

From Colin Barker, Jul 20 2017: (Start)

G.f.: x*(39 - 77*x + 111*x^2 - 88*x^3 + 36*x^4 - 6*x^5) / (1 - x)^7.

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 > 6.

(End)