A293611 a(n) = (25*n + 41)*Pochhammer(n, 5) / 6!.

0, 11, 91, 406, 1316, 3486, 8022, 16632, 31812, 57057, 97097, 158158, 248248, 377468, 558348, 806208, 1139544, 1580439, 2154999, 2893814, 3832444, 5011930, 6479330, 8288280, 10499580, 13181805, 16411941, 20276046, 24869936, 30299896, 36683416, 44149952, 52841712

Offset: 0

Author

Peter Luschny, Oct 13 2017

Keywords

• nonn
• easy

Links

• G. C. Greubel, 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).

Programs

Magma

[(25*n + 41)*(n+4)*(n+3)*(n+2)*(n+1)*n/Factorial(6):n in [0..50]]; // G. C. Greubel, Oct 22 2017

Maple

A293611:= n -> (25*n + 41)*pochhammer(n,5)/6!;
seq(A293611(n), n=0..29);

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0, 11, 91, 406, 1316, 3486, 8022}, 40] (* or *) a = 1/720 (984 #1 + 2650 #1^2 + 2685 #1^3 + 1285 #1^4 + 291 #1^5 + 25 #1^6) &; Table[a[n], {n, 0, 40}]
Table[(25*n + 41)*Pochhammer[n, 5]/6!, {n, 0, 50}] (* G. C. Greubel, Oct 22 2017 *)

PARI

for(n=0,50, print1((25*n + 41)*(n+4)*(n+3)*(n+2)*(n+1)*n/6!, ", ")) \\ G. C. Greubel, Oct 22 2017

PARI

concat(0, Vec(x*(11 + 14*x) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Jul 28 2019

Formula

From Colin Barker, Jul 28 2019: (Start)

G.f.: x*(11 + 14*x) / (1 - x)^7.

a(n) = (n*(984 + 2650*n + 2685*n^2 + 1285*n^3 + 291*n^4 + 25*n^5)) / 720.

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)