A293612 a(n) = (1/2)*(n + 1)*(5*n^2 + 15*n + 6)*Pochhammer(n, 6) / 6!.

0, 26, 588, 5376, 30660, 129780, 446292, 1315776, 3444012, 8198190, 18058040, 37285248, 72882264, 135925608, 243374040, 420468480, 703858344, 1145608002, 1818257364, 2821132160, 4288122300, 6397170780, 9381740940, 13544556480, 19273936500, 27063076950, 37532660256

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Programs

Magma

[(n + 1)*(5*n^2 + 15*n + 6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/(2*Factorial(6)):n in [0..50]]; // G. C. Greubel, Oct 22 2017

Maple

A293612 := n -> (1/2)*(n + 1)*(5*n^2 + 15*n + 6)*pochhammer(n,6)/6!;
seq(A293612(n), n=0..29);

Mathematica

LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0, 26, 588, 5376, 30660, 129780, 446292, 1315776, 3444012, 8198190}, 40] (* or *)
a = (720 #1 + 4164 #1^2 + 9504 #1^3 + 11315 #1^4 + 7745 #1^5 + 3146 #1^6 + 746 #1^7 + 95 #1^8 + 5 #1^9)/1440 &; Table[a[n], {n, 0, 40}]
Table[(n + 1)*(5*n^2 + 15*n + 6)*Pochhammer[n, 6]/(2*6!), {n, 0, 50}] (* G. C. Greubel, Oct 22 2017 *)

PARI

for(n=0,50, print1((n + 1)*(5*n^2 + 15*n + 6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/(2*6!), ", ")) \\ G. C. Greubel, Oct 22 2017

PARI

concat(0, Vec(2*x*(13 + 164*x + 333*x^2 + 120*x^3) / (1 - x)^10 + O(x^40))) \\ Colin Barker, Jul 28 2019

Formula

From Colin Barker, Jul 28 2019: (Start)

G.f.: 2*x*(13 + 164*x + 333*x^2 + 120*x^3) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9.

a(n) = ((n*(1+n)^2*(720 + 2724*n + 3336*n^2 + 1919*n^3 + 571*n^4 + 85*n^5 + 5*n^6))) / 1440.

(End)