A325287 - OEIS

%I #15 Oct 02 2019 05:19:51

%S 1,2,16,380,15280,842672,57985144,4735508672,445364211760,

%T 47281191656960,5586025249211056,726588091176753152,

%U 103169269785836042656,15880361395424986644320,2634307488850605478606240,468569833279898692863674720,88975116507316444085923086400,17966290253142630862386608565440,3844488506759131598435757854078080,869080066111317591084733034309229440,206969312517505574682143594517889278400

%N G.f. satisfies 1 = Sum_{n>=0} ((1+x)^(n*(n-1)/2) / A(x)^n) * (2^n/3^(n+1)).

%H Paul D. Hanna, <a href="/A325287/b325287.txt">Table of n, a(n) for n = 0..50</a>

%e G.f.: A(x) = 1 + 2*x + 16*x^2 + 380*x^3 + 15280*x^4 + 842672*x^5 + 57985144*x^6 + 4735508672*x^7 + 445364211760*x^8 + 47281191656960*x^9 + 5586025249211056*x^10 + ...

%t a[n_] := Module[{A}, A = {1}; Do[AppendTo[A, 0]; A[[-1]] = Round[ Coefficient[ Sum[(1+x + x*O[x]^Length[A])^(m*(m-1)/2)/(A.x^Range[0, Length[A] - 1])^m*2^m/3^(m + 1), {m, 0, 30 Length[A] + 200}]/2, x, Length[A] - 1]], {i, 1, n}]; Print[A[[n + 1]]]; A[[n + 1]]];

%t a /@ Range[0, 25] (* _Jean-François Alcover_, Oct 02 2019 *)

%o (PARI) /* Requires adequate precision */

%o \p500

%o {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = round( polcoeff( sum(m=0, 30*#A+200, (1+x+x*O(x^#A))^(m*(m-1)/2)/Ser(A)^m*2^m/3^(m+1)*1.)/2, #A-1))); A[n+1]}

%o for(n=0, 25, print1(a(n), ", "))

%Y Cf. A325286.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 23 2019

%E Added missing parentheses to definition. - _N. J. A. Sloane_, Aug 01 2019