A367234 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x))^4.

1, 1, 6, 35, 226, 1561, 11276, 84150, 643730, 5021038, 39781858, 319282210, 2590312872, 21208628405, 175024439504, 1454329099044, 12157356271998, 102170610282040, 862721635191860, 7315768816166027, 62274763166575410, 531950072655682896, 4558282056420235664

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Index entries for reversions of series

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).

From Seiichi Manyama, Dec 01 2024: (Start)

G.f.: exp( Sum_{k>=1} A378567(k) * x^k/k ).

a(n) = (1/(n+1)) * [x^n] 1/(1 - x/(1 - x)^4)^(n+1).

G.f.: (1/x) * Series_Reversion( x*(1 - x/(1 - x)^4) ). (End)

Prog

(PARI) a(n, s=4, t=2, u=1) = 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. A321798, A365114, A367235.

Cf. A001003, A011270, A365150.

Cf. A361306, A378567.

Sequence in context: A000399 A081051 A145145 * A357828 A347002 A346945

Adjacent sequences: A367231 A367232 A367233 * A367235 A367236 A367237

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2023

Status

approved