A384823 G.f. A(x) satisfies -1/x^11 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+6).

1, 1, 4, 28, 173, 1262, 9593, 75928, 618342, 5149640, 43650123, 375347585, 3266282211, 28709930633, 254526671024, 2273271614848, 20435110855838, 184745786960642, 1678668998195885, 15321962225034079, 140418372363945954, 1291587696225346583, 11919771215919819476, 110338977972166474055

Offset

0,3

Links

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

Formula

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

(1) -1/x^11 = Sum_{n=-oo..+oo} A(x)^n * x^n * (1 - x^n)^(n+6).

(2) -x = Sum_{n=-oo..+oo, n<>0} (-1/A(x))^n * x^((n-3)*(n-4)) / (1 - x^n)^(n-6).

a(n) ~ c * d^n / n^(3/2), where d = 9.887717015668710733345454711929087306... and c = 0.160435430066288197856237263106693... - Vaclav Kotesovec, Jun 11 2025

Example

G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 173*x^4 + 1262*x^5 + 9593*x^6 + 75928*x^7 + 618342*x^8 + 5149640*x^9 + 43650123*x^10 + ...

Prog

(PARI) {a(n) = my(A=[1, 1, 0, 0, 0]); for(i=1, n, A = concat(A, 0);
A[#A-3] = polcoeff( sum(m=-#A, #A, x^m * Ser(A)^m * (1 - x^m +x*O(x^n))^(m+6) ), #A-16)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A366731, A384821, A384822, A384824, A384825, A384826, A384827, A384828.

Sequence in context: A272456 A125687 A272791 * A291918 A223166 A026298

Adjacent sequences: A384820 A384821 A384822 * A384824 A384825 A384826

Keyword

nonn

Author

Paul D. Hanna, Jun 10 2025

Status

approved