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A183146 G.f.: Sum_{n>=0} [Sum_{k=0..n} C(n,k)^2*x^k]^3 * x^n.

%I A183146 #7 Mar 12 2022 13:26:01
%S A183146 1,1,4,16,80,407,2221,12380,71196,417016,2484839,15001779,91603298,
%T A183146 564661194,3509278042,21964437947,138330334357,875977578584,
%U A183146 5574225259696,35626247068500,228592067446715,1471959684881231
%N A183146 G.f.: Sum_{n>=0} [Sum_{k=0..n} C(n,k)^2*x^k]^3 * x^n.
%C A183146 Compare g.f. to a g.f. of the Whitney numbers in A051286:
%C A183146 Sum_{n>=0} [Sum_{k=0..n} C(n,k)^2*x^k] * x^n.
%e A183146 G.f.: A(x) = 1 + x + 4*x^2 + 16*x^3 + 80*x^4 + 407*x^5 + 2221*x^6 +...
%e A183146 which equals the sum of the series:
%e A183146 A(x) = 1 + (1 + x)^3*x + (1 + 4*x + x^2)^3*x^2
%e A183146 + (1 + 9*x + 9*x^2 + x^3)^3*x^3
%e A183146 + (1 + 16*x + 36*x^2 + 16*x^3 + x^4)^3*x^4
%e A183146 + (1 + 25*x + 100*x^2 + 100*x^3 + 25*x^4 + x^5)^3*x^5
%e A183146 + (1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)^3*x^6 +...
%o A183146 (PARI) {a(n)=polcoeff(sum(m=0,n,sum(k=0,m,binomial(m,k)^2*x^k)^3*x^m)+x*O(x^n),n)}
%Y A183146 Cf. A180717, A051286.
%K A183146 nonn
%O A183146 0,3
%A A183146 _Paul D. Hanna_, Dec 26 2010