A361771 Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(n-1).

1, 1, 1, 7, 28, 89, 421, 1898, 7912, 36412, 169960, 779139, 3668210, 17486938, 83333003, 400956919, 1943928504, 9455346485, 46225027071, 227066384875, 1119123274755, 5534782142253, 27463607765186, 136652474592260, 681728348606011, 3409395265172439, 17088672210734316

Offset

0,4

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 may be defined by the following.

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

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

Example

G.f.: A(x) = 1 + x + x^2 + 7*x^3 + 28*x^4 + 89*x^5 + 421*x^6 + 1898*x^7 + 7912*x^8 + 36412*x^9 + 169960*x^10 + 779139*x^11 + 3668210*x^12 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A361772, A361773, A361774.

Cf. A355865, A357227, A359712, A357232.

Sequence in context: A117473 A163037 A224153 * A276236 A022572 A193654

Adjacent sequences: A361768 A361769 A361770 * A361772 A361773 A361774

Keyword

nonn

Author

Paul D. Hanna, May 13 2023

Status

approved