A060061 Fourth column of triangle A060058.

61, 1385, 12284, 68060, 281210, 948002, 2749340, 7097948, 16700255, 36419955, 74551048, 144631240, 267951892, 476948260, 819683560, 1365672424, 2213323585, 3499318141, 5410278500, 8197124100

Offset: 0

Author

Wolfdieter Lang, Mar 16 2001

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000330, A060060.

Programs

Mathematica

Table[Binomial[n+6,6]*(280*n^3+2436*n^2+5906n+3843)/63,{n,0,19}] (* Indranil Ghosh, Feb 21 2017 *)

Python

import math
def C(n, r):
    f=math.factorial
    return f(n)//f(r)//f(n-r)
def A060061(n):
    return (C(n+6, 6)*(280*n**3+2436*n**2+5906*n+3843))//63 # Indranil Ghosh, Feb 21 2017

Formula

a(n) = Sum_{j3=1..n+1} j3^2*Sum_{j2=1..j3+1} j2^2*Sum_{j1=1..j2+1} j1^2.

a(n) = A060058(n+3, 3) = binomial(n+6, 6)*(280*n^3+2436*n^2+5906*n+3843)/(7*9).

G.f.: (61+775*x+1179*x^2+225*x^3)/(1-x)^10 = p(3, x)/(1-x)^(3*3+1) with p(3, x)=sum(A060063(3, m)*x^m, m=0..3).