A367240 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^2)^3.

1, 1, 5, 29, 192, 1372, 10314, 80390, 643774, 5264984, 43788393, 369221844, 3149085162, 27119598885, 235495141963, 2059677411141, 18127763268114, 160433599528417, 1426870597505859, 12746368353418175, 114316604199957112, 1028937342955189009

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).

Prog

(PARI) a(n, s=3, t=2, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));

Crossrefs

Cf. A001764, A367239, A367241.

Sequence in context: A113713 A142980 A062191 * A171267 A258314 A225030

Adjacent sequences: A367237 A367238 A367239 * A367241 A367242 A367243

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved