A359923 a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n.

1, 1, 6, 15, 69, 376, 1741, 8860, 46044, 245074, 1336538, 7337135, 40736876, 228625148, 1293530435, 7372491383, 42275811853, 243742895280, 1412310750812, 8219298313118, 48023377286364, 281592177442072, 1656522460985914, 9773791391488278, 57824226906859849

Offset

0,3

Links

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

Formula

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

(1) x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n.

(2) x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(n*(n-1)) * A(x)^(n^2) / (1 + 3*x^n*A(x)^n)^n.

Example

G.f.: A(x) = 1 + x + 6*x^2 + 15*x^3 + 69*x^4 + 376*x^5 + 1741*x^6 + 8860*x^7 + 46044*x^8 + 245074*x^9 + 1336538*x^10 + ...
where
x = ... + x^6*A(x)^9/(1 + 3*x^3*A(x)^3)^3 - x^2*A(x)^4/(1 + 3*x^2*A(x)^2)^2 + A(x)/(1 + 3*x*A(x)) - 1 + x*(3 + x*A(x)) - x^2*(3 + x^2*A(x)^2)^2 + x^3*(3 + x^3*A(x)^3)^3 + ... + (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n + ...

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-1) * x^m * (3 + (x*Ser(A))^m)^m ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A359672, A359922.

Sequence in context: A298374 A324973 A318555 * A035077 A032164 A177122

Adjacent sequences: A359920 A359921 A359922 * A359924 A359925 A359926

Keyword

nonn

Author

Paul D. Hanna, Jan 18 2023

Status

approved