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%I #7 May 11 2019 17:56:30
%S 1,3,15,67,336,1767,9873,58221,360930,2345469,15926115,112702725,
%T 829218143,6329731749,50032666719,408810685879,3447546750090,
%U 29963861568735,268051909321565,2465213070499965,23282355990573738,225577403162464915,2240023319131286013,22778185448591006709,236997065442660095669,2521130509681288754841,27401150807636634911205,304071227823781106763523,3443058535424619400592874
%N G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * x^n * (1+x)^(n*(n+2)).
%C Equals column 2 of triangle A325580.
%e G.f.: A(x) = 1 + 3*x + 15*x^2 + 67*x^3 + 336*x^4 + 1767*x^5 + 9873*x^6 + 58221*x^7 + 360930*x^8 + 2345469*x^9 + 15926115*x^10 + 112702725*x^11 + ...
%e such that
%e A(x) = 1 + 3*x*(1+x)^3 + 6*x^2*(1+x)^8 + 10*x^3*(1+x)^15 + 15*x^4*(1+x)^24 + 21*x^5*(1+x)^35 + 28*x^6*(1+x)^48 + 36*x^7*(1+x)^63 + 45*x^8*(1+x)^80 + ...
%o (PARI) {a(n) = my(A = sum(m=0, n, (m+1)*(m+2)/2 * x^m * (1+x +x*O(x^n))^(m*(m+2)) )); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A325580, A121689, A325581, A325587.
%K nonn
%O 0,2
%A _Paul D. Hanna_, May 11 2019
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