A325287 G.f. satisfies 1 = Sum_{n>=0} ((1+x)^(n*(n-1)/2) / A(x)^n) * (2^n/3^(n+1)).

1, 2, 16, 380, 15280, 842672, 57985144, 4735508672, 445364211760, 47281191656960, 5586025249211056, 726588091176753152, 103169269785836042656, 15880361395424986644320, 2634307488850605478606240, 468569833279898692863674720, 88975116507316444085923086400, 17966290253142630862386608565440, 3844488506759131598435757854078080, 869080066111317591084733034309229440, 206969312517505574682143594517889278400

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..50

Example

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 + ...

Mathematica

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]]];
a /@ Range[0, 25] (* Jean-François Alcover, Oct 02 2019 *)

Prog

(PARI) /* Requires adequate precision */
\p500
{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]}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A325286.

Sequence in context: A015201 A227406 A068471 * A140308 A280723 A052737

Adjacent sequences: A325284 A325285 A325286 * A325288 A325289 A325290

Keyword

nonn

Author

Paul D. Hanna, Apr 23 2019

Extensions

Added missing parentheses to definition. - N. J. A. Sloane, Aug 01 2019

Status

approved