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A367639

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

1, 3, 6, 16, 52, 184, 688, 2672, 10672, 43552, 180800, 761088, 3241088, 13937408, 60435968, 263962880, 1160188672, 5127762432, 22775636992, 101608357888, 455105255424, 2045751037952, 9225923895296, 41731062358016, 189275050729472, 860630181167104

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

G.f.: A(x) = 2*(1+x)^2 / (1+sqrt(1-4*x*(1+x))).

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

a(n) ~ 2^(n - 5/4) * (1 + sqrt(2))^(n + 3/2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Nov 25 2023

D-finite with recurrence (n+1)*a(n) +(-3*n+1)*a(n-1) +2*(-4*n+9)*a(n-2) +4*(-n+4)*a(n-3)=0. - R. J. Mathar, Dec 04 2023

From Peter Bala, May 05 2024: (Start)

A(x) = (1 + x)*S(x/(1 + x)), where S(x) = (1 - x - sqrt(1 - 6*x + x^2))/(2*x) is the g.f. of the large Schröder numbers A006318. Cf. A025227.

A333090(n) = [x^n] A(x)^n. (End)

PROG

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

CROSSREFS

Cf. A006318, A025227, A367640, A333090, A367641.

Sequence in context: A378801 A274294 A201969 * A391837 A340498 A288850

Adjacent sequences: A367636 A367637 A367638 * A367640 A367641 A367642

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Nov 25 2023

STATUS

approved

URL: https://oeis.org/A367639

⇱ A367639 - OEIS