A361775 Expansion of g.f. A(x) satisfying x = Sum_{n=-oo..+oo} (-1)^n * x^n * A(x)^n * (A(x)^n + x^n)^n.

1, 1, 5, 21, 95, 405, 1680, 6926, 28257, 115254, 471785, 1908622, 7444553, 27617809, 101165030, 411727344, 1980777419, 9377434309, 30465401498, 5465053256, -319249451709, 3800908753389, 79369582680985, 507720631888326, -779604798853789, -39876367011094054

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..201

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.

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

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

Example

G.f.: A(x) = 1 + x + 5*x^2 + 21*x^3 + 95*x^4 + 405*x^5 + 1680*x^6 + 6926*x^7 + 28257*x^8 + 115254*x^9 + 471785*x^10 + ...

Prog

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

Crossrefs

Cf. A361776, A292088.

Sequence in context: A103519 A178876 A202513 * A343349 A159289 A201869

Adjacent sequences: A361772 A361773 A361774 * A361776 A361777 A361778

Keyword

sign

Author

Paul D. Hanna, May 08 2023

Status

approved