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A060061 Fourth column of triangle A060058.

%I A060061 #18 Jan 07 2025 01:59:51
%S A060061 61,1385,12284,68060,281210,948002,2749340,7097948,16700255,36419955,
%T A060061 74551048,144631240,267951892,476948260,819683560,1365672424,
%U A060061 2213323585,3499318141,5410278500,8197124100
%N A060061 Fourth column of triangle A060058.
%H A060061 Indranil Ghosh, <a href="/A060061/b060061.txt">Table of n, a(n) for n = 0..5000</a>
%F A060061 a(n) = Sum_{j3=1..n+1} j3^2*Sum_{j2=1..j3+1} j2^2*Sum_{j1=1..j2+1} j1^2.
%F A060061 a(n) = A060058(n+3, 3) = binomial(n+6, 6)*(280*n^3+2436*n^2+5906*n+3843)/(7*9).
%F A060061 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).
%t A060061 Table[Binomial[n+6,6]*(280*n^3+2436*n^2+5906n+3843)/63,{n,0,19}] (* _Indranil Ghosh_, Feb 21 2017 *)
%o A060061 (Python)
%o A060061 import math
%o A060061 def C(n, r):
%o A060061     f=math.factorial
%o A060061     return f(n)//f(r)//f(n-r)
%o A060061 def A060061(n):
%o A060061     return (C(n+6, 6)*(280*n**3+2436*n**2+5906*n+3843))//63 # _Indranil Ghosh_, Feb 21 2017
%Y A060061 Cf. A000330, A060060.
%K A060061 nonn,easy
%O A060061 0,1
%A A060061 _Wolfdieter Lang_, Mar 16 2001