A369722 Expansion of e.g.f. exp( (3/2) * (1-sqrt(1-4*x)) ).

1, 3, 15, 117, 1305, 19323, 359559, 8084205, 213425361, 6475518675, 222088463199, 8497641269637, 358899729493545, 16585866328129803, 832523413971932055, 45105537151437499197, 2623613865509122341921, 163070009495928522691875

Offset: 0

Author

Seiichi Manyama, Jan 30 2024

Keywords

• nonn

Crossrefs

Cf. A001517, A101682, A243953, A369723, A369724.

Cf. A000108.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3/2*(1-sqrt(1-4*x)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} 3^(n-k) * (n-1+k)! / (k! * (n-1-k)!).

a(n) = 2*(2*n-3)*a(n-1) + 9*a(n-2).