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A321606 G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(3*n^2) / A(x)^(n^2). 1
1, 1, 3, 7, 25, 80, 342, 1818, 11502, 86626, 707359, 6202212, 57655266, 563021626, 5762459074, 61582852498, 685183190074, 7919267757340, 94878751361581, 1176171409288897, 15062758843882271, 198997851380457874, 2708587403764115335, 37938389537270197751, 546245195916221529029, 8076733428378707580710, 122523819509730133116908, 1905311108531544568628670 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note that if G(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / G(x)^(n^2), then G(x) has negative coefficients.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..200

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 25*x^4 + 80*x^5 + 342*x^6 + 1818*x^7 + 11502*x^8 + 86626*x^9 + 707359*x^10 + 6202212*x^11 + 57655266*x^12 + ...

such that

A(x) = 1 + x*(1+x)^3/A(x) + x^2*(1+x)^12/A(x)^4 + x^3*(1+x)^27/A(x)^9 + x^4*(1+x)^48/A(x)^16 + x^5*(1+x)^75/A(x)^25 + x^6*(1+x)^108/A(x)^36 + ...

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))^(4*n^2)/Ser(A)^(n^2+1) ), #A-1) ); A[n+1]}

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

CROSSREFS

Sequence in context: A148733 A148734 A124425 * A118398 A047974 A148735

Adjacent sequences:  A321603 A321604 A321605 * A321607 A321608 A321609

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 23 2018

STATUS

approved

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Last modified January 21 22:47 EST 2020. Contains 331129 sequences. (Running on oeis4.)