A394772 G.f. A(x) satisfies A(x) = 1 - x * d/dx log(1 - x*A(x)^2).

1, 1, 5, 40, 421, 5381, 80084, 1352996, 25514085, 530585995, 12057511165, 297262043728, 7903318125772, 225459841731580, 6870875386884248, 222821822838984140, 7663159283027280677, 278621900555627573303, 10679748481505102835791, 430464260837712074057624

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..402

Formula

G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 + x^2*d/dx(A(x)^2).

a(0) = 1; a(n) = (n-1) * Sum_{k=0..n-1} a(k) * a(n-1-k) + Sum_{i, j, k>=0 and i+j+k=n-1} a(i) * a(j) * a(k).

a(n) ~ c * 2^n * n^(n + 3/2) / exp(n), where c = 0.95905269684565180280034696... - Vaclav Kotesovec, Apr 01 2026

Crossrefs

Cf. A003319, A027307, A159607.

Cf. A394778, A394779.

Cf. A394780, A394781.

Sequence in context: A375456 A383375 A083304 * A375954 A375953 A208248

Adjacent sequences: A394769 A394770 A394771 * A394773 A394774 A394775

Keyword

nonn

Author

Seiichi Manyama, Apr 01 2026

Status

approved