cp's OEIS Frontend

A325581 G.f.: Sum_{n>=0} (n+1) * x^n * (1+x)^(n*(n+1)).

%I A325581 #10 May 11 2019 17:56:04
%S A325581 1,2,7,24,98,430,2062,10610,58240,338984,2081189,13423258,90626012,
%T A325581 638509008,4682120763,35650040782,281266115870,2295142774336,
%U A325581 19338107378888,167987656339604,1502475101768767,13818574571596432,130542011977462175,1265358001625542030,12572822521590475349,127943980062492526520,1332336499429857507073,14186629118985647254622,154348478009342665050329,1714707987491310848285920
%N A325581 G.f.: Sum_{n>=0} (n+1) * x^n * (1+x)^(n*(n+1)).
%C A325581 Equals column 1 of triangle A325580.
%e A325581 G.f.: A(x) = 1 + 2*x + 7*x^2 + 24*x^3 + 98*x^4 + 430*x^5 + 2062*x^6 + 10610*x^7 + 58240*x^8 + 338984*x^9 + 2081189*x^10 + 13423258*x^11 + 90626012*x^12 + ...
%e A325581 such that
%e A325581 A(x) = 1 + 2*x*(1+x)^2 + 3*x^2*(1+x)^6 + 4*x^3*(1+x)^12 + 5*x^4*(1+x)^20 + 6*x^5*(1+x)^30 + 7*x^6*(1+x)^42 + 8*x^7*(1+x)^(56) + 9*x^8*(1+x)^72 + ...
%o A325581 (PARI) {a(n) = my(A = sum(m=0,n, (m+1) * x^m * (1+x +x*O(x^n))^(m*(m+1)) )); polcoeff(A,n)}
%o A325581 for(n=0,30, print1(a(n),", "))
%Y A325581 Cf. A325580, A121689, A325586, A325587.
%K A325581 nonn
%O A325581 0,2
%A A325581 _Paul D. Hanna_, May 11 2019