A370473 G.f. satisfies A(x) = 1 + x * A(x)^2 * (1 - A(x) + A(x)^2 - A(x)^3 + A(x)^4).

1, 1, 4, 25, 185, 1501, 12914, 115723, 1068505, 10094770, 97117624, 948181724, 9370734322, 93562986440, 942385174150, 9563720899515, 97696642766654, 1003789888620166, 10366477185870960, 107548800153957745, 1120374840689934195, 11714707429579539268

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

G.f. A(x) satisfies:

(1) A(x)^2 = 1 + x * A(x)^2 * (1 + A(x)^5).

(2) A(x) = sqrt(B(x)) where B(x) is the g.f. of A366401.

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

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n+5*k/2+1/2, n)/(2*n+5*k+1));

Crossrefs

Cf. A000108, A219537.

Cf. A370472, A370476.

Cf. A366401.

Sequence in context: A364759 A246539 A367017 * A369479 A166697 A054368

Adjacent sequences: A370470 A370471 A370472 * A370474 A370475 A370476

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2024

Status

approved