A321099 G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n * (1+x)^(n^2) / A(x)^(n*(n+1)/2).

1, 1, 1, 1, 1, 1, 2, 5, 18, 61, 229, 879, 3588, 15283, 68029, 314985, 1512982, 7523664, 38653397, 204844184, 1118152388, 6278617770, 36225373016, 214531854676, 1302820719810, 8106006393514, 51629965051190, 336384879743751, 2240263173545424, 15240406795991028, 105840760976497158, 749907226527126570

Offset

0,7

Comments

Compare to: G(x) = Sum_{n>=0} x^n * (1+x)^(n^2) / G(x)^(n*(n+1)) when G(x) = 1+x.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + 2*x^6 + 5*x^7 + 18*x^8 + 61*x^9 + 229*x^10 + 879*x^11 + 3588*x^12 + 15283*x^13 + 68029*x^14 + ...
such that
A(x) = 1 + x*(1+x)/A(x) + x^2*(1+x)^4/A(x)^3 + x^3*(1+x)^9/A(x)^6 + x^4*(1+x)^16/A(x)^10 + x^5*(1+x)^25/A(x)^15 + x^6*(1+x)^36/A(x)^21 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(n=0, #A, x^n*(1+x +x*O(x^#A))^(n^2)/Ser(A)^(n*(n+1)/2) ), #A-1)); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A286317 A303174 A148426 * A241894 A148427 A068000

Adjacent sequences: A321096 A321097 A321098 * A321100 A321101 A321102

Keyword

nonn

Author

Paul D. Hanna, Nov 20 2018

Status

approved