A325586 G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * x^n * (1+x)^(n*(n+2)).

1, 3, 15, 67, 336, 1767, 9873, 58221, 360930, 2345469, 15926115, 112702725, 829218143, 6329731749, 50032666719, 408810685879, 3447546750090, 29963861568735, 268051909321565, 2465213070499965, 23282355990573738, 225577403162464915, 2240023319131286013, 22778185448591006709, 236997065442660095669, 2521130509681288754841, 27401150807636634911205, 304071227823781106763523, 3443058535424619400592874

Offset: 0

Author

Paul D. Hanna, May 11 2019

Keywords

• nonn

Comments

Equals column 2 of triangle A325580.

Examples

			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 + ...
such that
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 + ...
		

Crossrefs

Cf. A325580, A121689, A325581, A325587.

Programs

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)}
for(n=0, 30, print1(a(n), ", "))