A384828 G.f. A(x) satisfies 1/x^71 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+16).

1, 1, 9, 120, 1839, 30862, 548783, 10160786, 193811734, 3782270289, 75158649892, 1515578476370, 30935212293083, 637920390487505, 13269865608471203, 278121828806207328, 5867506406619195047, 124502776024601555996, 2655381364988431518262, 56892952987400631546208, 1223972213493916563960331

Offset: 0

Author

Paul D. Hanna, Jun 10 2025

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 9*x^2 + 120*x^3 + 1839*x^4 + 30862*x^5 + 548783*x^6 + 10160786*x^7 + 193811734*x^8 + 3782270289*x^9 + 75158649892*x^10 + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A366731, A384821, A384822, A384823, A384824, A384825, A384826, A384827.

Programs

PARI

{a(n) = my(A=[1,1,0,0,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-8] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+16) ), #A-81)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.

(1) 1/x^71 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+16).

(2) x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-8)*(n-9)) / (1 - x^n)^(n-16).

a(n) ~ c * d^n / n^(3/2), where d = 23.2218466497883684132359544378917382382303363986... and c = 0.05318473987345007866210446949223464954972731... - Vaclav Kotesovec, Jun 11 2025