A381570 G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^3.

1, 3, 12, 82, 732, 7944, 99156, 1381464, 21065853, 346932822, 6112226961, 114383442888, 2261347164766, 47025363829497, 1025005545866361, 23349137897005296, 554467427766694440, 13696046757037152183, 351231525904387758222, 9335221780768641038952

Offset: 0

Author

Seiichi Manyama, Feb 28 2025

Keywords

• nonn

Crossrefs

Column k=1 of A381569.

Cf. A087949, A120972, A212029, A381568, A381574.

Programs

PARI

a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-3*j+3*k, j)/(n-j+k)*a(n-j, j)));

Formula

See A381569.

G.f.: B(x)^3, where B(x) is the g.f. of A212029.