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A060060 Third column of triangle A060058.

%I A060060 #13 Dec 18 2024 19:07:43
%S A060060 5,61,331,1211,3486,8526,18522,36762,67947,118547,197197,315133,
%T A060060 486668,729708,1066308,1523268,2132769,2933049,3969119,5293519,
%U A060060 6967114,9059930,11652030,14834430,18710055,23394735
%N A060060 Third column of triangle A060058.
%H A060060 Indranil Ghosh, <a href="/A060060/b060060.txt">Table of n, a(n) for n = 0..5000</a>
%F A060060 a(n) = A060058(n+2, 2) = binomial(n+4, 4)*(20*n^2+88*n+75)/(3*5).
%F A060060 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).
%e A060060 a(3) = binomial(7,4) * (20 * 3^2 + 88*3 +75) / 15 = (35 * 519)/15 = 1211. - _Indranil Ghosh_, Feb 21 2017
%t A060060 Table[(Binomial[n+4,4]*(20*n^2+88*n+75)/15),{n,0,25}] (* _Indranil Ghosh_, Feb 21 2017 *)
%o A060060 (Python)
%o A060060 import math
%o A060060 def C(n, r):
%o A060060     f=math.factorial
%o A060060     return f(n)//f(r)//f(n-r)
%o A060060 def A060060(n):
%o A060060     return C(n+4, 4)*(20*n**2+88*n+75)//15 # _Indranil Ghosh_, Feb 21 2017
%K A060060 nonn,easy
%O A060060 0,1
%A A060060 _Wolfdieter Lang_, Mar 16 2001