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

0,1

Links

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

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A000330, A060060.

Sequence in context: A218112 A154428 A262017 * A000507 A350974 A143011

Adjacent sequences: A060058 A060059 A060060 * A060062 A060063 A060064

Keyword

nonn,easy,changed

Author

Wolfdieter Lang, Mar 16 2001

Status

approved