close
login
A365135
G.f. A(x) satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^3)^2.
1
1, 2, 11, 68, 467, 3418, 26133, 206264, 1667908, 13746476, 115050074, 975180582, 8354044986, 72215867960, 629139381448, 5518236646614, 48689379017014, 431868759238498, 3848616161600778, 34441553184113542, 309390614528633311, 2788841905397090626
OFFSET
0,2
FORMULA
If g.f. satisfies A(x) = (1 + x*A(x)/(1 - x*A(x))^s)^t, then a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(t*(n+1),k) * binomial(n+(s-1)*k-1,n-k).
From Seiichi Manyama, Oct 10 2025: (Start)
G.f.: (1/x) * Series_Reversion( x / (1 + x / (1 - x)^3)^2 ).
G.f.: B(x)^2, where B(x) is the g.f. of A367240. (End)
PROG
(PARI) a(n, s=3, t=2) = sum(k=0, n, binomial(t*(n+1), k)*binomial(n+(s-1)*k-1, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 23 2023
STATUS
approved