A371538 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1+x))^3.

1, 3, 18, 151, 1440, 14835, 160793, 1806849, 20859129, 245905348, 2947869600, 35825319390, 440372147956, 5465555197818, 68396554601013, 862066323857486, 10933638171672105, 139439595024315675, 1787056241039876890, 23003636498360053905, 297283046361025602900

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = 3 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+3,k)/(6*k+3).

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349362.

Prog

(PARI) a(n) = 3*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+3, k)/(6*k+3));

Crossrefs

Cf. A349362, A371537, A371539, A371540, A371541.

Cf. A371522.

Sequence in context: A200320 A352850 A347020 * A207569 A005412 A352647

Adjacent sequences: A371535 A371536 A371537 * A371539 A371540 A371541

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2024

Status

approved