A392977 Expansion of (1/x) * Series_Reversion( x * ((1-x^2)^3 - x) ).

1, 1, 5, 20, 101, 525, 2887, 16359, 95115, 563838, 3395642, 20716254, 127764434, 795256210, 4989327246, 31518412352, 200311909083, 1279869928686, 8216519744870, 52973522292775, 342843762187861, 2226606216608385, 14506570969312335, 94785565057725600

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

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

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n-2*k,n) * binomial(6*n-5*k+2,k).

Mathematica

Table[1/(n+1)*Sum[Binomial[2*n-2*k, n]*Binomial[6*n-5*k+2, k], {k, 0, Floor[n/2]}], {n, 0, 24}] (* Vincenzo Librandi, Jan 31 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(2*n-2*k, n)*binomial(6*n-5*k+2, k))/(n+1);
(Magma) [1/(n+1) * &+[Binomial(2*n-2*k, n)* Binomial(6*n-5*k+2, k) : k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Jan 31 2026

Crossrefs

Cf. A001002, A370839, A392976.

Sequence in context: A108509 A110595 A369488 * A092640 A165961 A276314

Adjacent sequences: A392974 A392975 A392976 * A392978 A392979 A392980

Keyword

nonn

Author

Seiichi Manyama, Jan 29 2026

Status

approved