A293613 a(n) = (1/4)*(7*n + 17)*(5*n + 6)*Pochhammer(n, 6) / 6!.

0, 66, 868, 5586, 24570, 84630, 245322, 625086, 1440582, 3063060, 6096090, 11479468, 20624604, 35587188, 59283420, 95756580, 150501204, 230852622, 346450104, 509782350, 736824550, 1047776730, 1467913590, 2028556530, 2768179050, 3733657200, 4981677246, 6580313208

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 (9,-36,84,-126,126,-84,36,-9,1).

Programs

Magma

[(7*n + 17)*(5*n + 6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/(4*Factorial(6)): n in [0..50]]; // G. C. Greubel, Oct 23 2017

Maple

A293613 := n -> (1/4)*(7*n + 17)*(5*n + 6)*pochhammer(n,6)/6!;
seq(A293613(n), n=0..29);

Mathematica

LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {0, 66, 868, 5586, 24570, 84630, 245322, 625086, 1440582}, 40] (* or *) a = (12240 #1 + 43188 #1^2 + 61948 #1^3 + 46835 #1^4 + 20200 #1^5 + 4982 #1^6 + 652 #1^7 + 35 #1^8)/2880 & ; Table[a[n], {n, 0, 40}]
Table[(7*n + 17)*(5*n + 6)*Pochhammer[n, 6]/(4*6!), {n, 0, 50}] (* G. C. Greubel, Oct 23 2017 *)

PARI

for(n=0,50, print1((7*n + 17)*(5*n + 6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/(4*6!), ", ")) \\ G. C. Greubel, Oct 23 2017

PARI

concat(0, Vec(2*x*(33 + 137*x + 75*x^2) / (1 - x)^9 + O(x^40))) \\ Colin Barker, Jul 28 2019

Formula

From Colin Barker, Jul 28 2019: (Start)

G.f.: 2*x*(33 + 137*x + 75*x^2) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

a(n) = ((n*(12240 + 43188*n + 61948*n^2 + 46835*n^3 + 20200*n^4 + 4982*n^5 + 652*n^6 + 35*n^7))) / 2880.

(End)