A394842 G.f. A(x) satisfies A(x) = 1 / (1 - x * d/dx log(1 + x*A(x)^2)).

1, 1, 4, 29, 290, 3598, 52558, 876973, 16393490, 338723774, 7659314448, 188081598562, 4984170966084, 141791087406976, 4310763278116930, 139505813689497901, 4788945945093822514, 173832767722363540646, 6653265128970512012968, 267812427414947002326438

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

a(0) = 1; a(n) = Sum_{k=0..n-1} a(k)*a(n-1-k) + 2*(n-1)/3 * Sum_{i, j, k>=0 and i+j+k=n-1} a(i)*a(j)*a(k).

Crossrefs

Cf. A075834.

Sequence in context: A302586 A302609 A181197 * A217807 A348651 A360584

Adjacent sequences: A394839 A394840 A394841 * A394843 A394844 A394845

Keyword

nonn

Author

Seiichi Manyama, Apr 04 2026

Status

approved