A060060 Third column of triangle A060058.

5, 61, 331, 1211, 3486, 8526, 18522, 36762, 67947, 118547, 197197, 315133, 486668, 729708, 1066308, 1523268, 2132769, 2933049, 3969119, 5293519, 6967114, 9059930, 11652030, 14834430, 18710055, 23394735

Offset: 0

Author

Wolfdieter Lang, Mar 16 2001

Keywords

• nonn
• easy

Examples

			a(3) = binomial(7,4) * (20 * 3^2 + 88*3 +75) / 15 = (35 * 519)/15 = 1211. - _Indranil Ghosh_, Feb 21 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..5000

Programs

Mathematica

Table[(Binomial[n+4,4]*(20*n^2+88*n+75)/15),{n,0,25}] (* Indranil Ghosh, Feb 21 2017 *)

Python

import math
def C(n, r):
    f=math.factorial
    return f(n)//f(r)//f(n-r)
def A060060(n):
    return C(n+4, 4)*(20*n**2+88*n+75)//15 # Indranil Ghosh, Feb 21 2017

Formula

a(n) = A060058(n+2, 2) = binomial(n+4, 4)*(20*n^2+88*n+75)/(3*5).

G.f.: (5+26*x+9*x^2)/(1-x)^7 = p(2, x)/(1-x)^(2*3+1). p(2, x)=sum(A060063(2, m)*x^m, m=0..2).