A366556 G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^3.

1, 1, 0, 0, 1, 3, 3, 1, 3, 15, 30, 30, 27, 87, 252, 420, 475, 747, 2064, 4632, 7203, 9933, 19635, 47025, 92013, 144745, 237510, 498498, 1073817, 1969131, 3267411, 5977881, 12462579, 25035747, 45090936, 79414344, 153115299, 311198457, 600883569, 1090988379, 2012793705

Offset

0,6

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(2*k+1,n-4*k) * binomial(3*k,k)/(2*k+1).

a(n) = A366592(n) + A366592(n-1).

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(2*k+1, n-4*k)*binomial(3*k, k)/(2*k+1));

Crossrefs

Cf. A019497, A366266, A366555.

Cf. A366554, A366558.

Cf. A366592.

Sequence in context: A277103 A120919 A032240 * A275625 A331901 A306148

Adjacent sequences: A366553 A366554 A366555 * A366557 A366558 A366559

Keyword

nonn

Author

Seiichi Manyama, Oct 13 2023

Status

approved