A371541 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^6.

1, 6, 45, 410, 4110, 43746, 485237, 5547396, 64901670, 773296320, 9350929395, 114464359296, 1415620823147, 17661466502796, 222017667461685, 2809362871991380, 35755481454362355, 457410181217186886, 5878378983480722222, 75856853080508789406

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A349362.

Prog

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

Crossrefs

Cf. A349362, A371537, A371538, A371539, A371540.

Cf. A371521.

Sequence in context: A365184 A135148 A137974 * A291421 A001879 A019577

Adjacent sequences: A371538 A371539 A371540 * A371542 A371543 A371544

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2024

Status

approved