A384826 G.f. A(x) satisfies 1/x^41 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+12).

1, 1, 7, 73, 861, 11112, 151828, 2159179, 31627690, 473917665, 7230164079, 111926802631, 1753762735460, 27760507986844, 443257137593369, 7130838718144623, 115469073853104486, 1880570694656739472, 30784302913287253256, 506228988080918570208, 8358750672258509735440, 138528877561300962357350

Offset: 0

Author

Paul D. Hanna, Jun 10 2025

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 7*x^2 + 73*x^3 + 861*x^4 + 11112*x^5 + 151828*x^6 + 2159179*x^7 + 31627690*x^8 + 473917665*x^9 + 7230164079*x^10 + ...
		

Links

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

Crossrefs

Cf. A366731, A384821, A384822, A384823, A384824, A384825, A384827, A384828.

Programs

PARI

{a(n) = my(A=[1,1,0,0,0,0,0,0]); for(i=1, n, A = concat(A, 0);
A[#A-6] = -polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+12) ), #A-49)); 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^41 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+12).

(2) x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-6)*(n-7)) / (1 - x^n)^(n-12).

a(n) ~ c * d^n / n^(3/2), where d = 17.821078213117779013059276484226766696509894506... and c = 0.072486824411461280676499747682168909434267... - Vaclav Kotesovec, Jun 11 2025