A293610 a(n) = (15*n^2 + 35*n + 16)*Pochhammer(n, 5) / 6!.

0, 11, 146, 896, 3696, 11886, 32172, 76692, 165792, 331617, 622622, 1109108, 1889888, 3100188, 4920888, 7589208, 11410944, 16774359, 24165834, 34187384, 47576144, 65225930, 88210980, 117811980, 155544480, 203189805, 262828566, 336876876, 428125376, 539781176

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 (8,-28,56,-70,56,-28,8,-1).

Programs

Magma

[(15*n^2 + 35*n + 16)*(n+4)*(n+3)*(n+2)*(n+1)*n/Factorial(6):n in [0..50]]; // G. C. Greubel, Oct 22 2017

Maple

A293610 := n -> (15*n^2 + 35*n + 16)*pochhammer(n,5)/6!:
seq(A293610(n), n=0..29);

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {0,11,146, 896, 3696, 11886, 32172, 76692}, 40] (* or *) a = (1/720)*(384*#1 + 1640*#1^2 + 2670*#1^3 + 2135*#1^4 + 891*#1^5 + 185*#1^6 + 15*#1^7) & ; Table[a[n], {n, 0, 40}]
Table[(15*n^2 + 35*n + 16)*Pochhammer[n, 5]/6!, {n, 0, 50}] (* G. C. Greubel, Oct 22 2017 *)

PARI

for(n=0,50, print1((15*n^2 + 35*n + 16)*(n+4)*(n+3)*(n+2)*(n+1)*n/6!, ", ")) \\ G. C. Greubel, Oct 22 2017

PARI

concat(0, Vec(x*(11 + 58*x + 36*x^2) / (1 - x)^8 + O(x^40))) \\ Colin Barker, Jul 28 2019

Formula

From Colin Barker, Jul 28 2019: (Start)

G.f.: x*(11 + 58*x + 36*x^2) / (1 - x)^8.

a(n) = (n*(384 + 1640*n + 2670*n^2 + 2135*n^3 + 891*n^4 + 185*n^5 + 15*n^6)) / 720.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

(End)