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%I #3 May 11 2019 14:51:43
%S 1,4,26,144,861,5300,33974,226716,1572134,11318196,84460828,652359324,
%T 5207769776,42909334344,364439847976,3186742207624,28656418042704,
%U 264722157073936,2509700822675234,24395793491141136,242936835660951240,2476311278424167804,25817877582760234776,275124609022178797944,2994612410107793787156,33272066553220515090708,377127538637173442895684,4358346743099457288466696
%N G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n * (1+x)^(n*(n+3)).
%C Equals column 3 of triangle A325580.
%e G.f.: A(x) = 1 + 4*x + 26*x^2 + 144*x^3 + 861*x^4 + 5300*x^5 + 33974*x^6 + 226716*x^7 + 1572134*x^8 + 11318196*x^9 + 84460828*x^10 + 652359324*x^11 + ...
%e such that
%e A(x) = 1 + 4*x*(1+x)^4 + 10*x^2*(1+x)^10 + 20*x^3*(1+x)^18 + 35*x^4*(1+x)^28 + 56*x^5*(1+x)^40 + 84*x^6*(1+x)^54 + 120*x^7*(1+x)^70 + 165*x^8*(1+x)^88 + ...
%o (PARI) {a(n) = my(A = sum(m=0, n, (m+1)*(m+2)*(m+3)/3! * x^m * (1+x +x*O(x^n))^(m*(m+3)) )); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%K nonn
%O 0,2
%A _Paul D. Hanna_, May 11 2019