A112328 a(n) = (n+1)*binomial(2n+2,n+1)-3*4^n+binomial(2n,n).

2, 18, 108, 562, 2724, 12660, 57240, 253842, 1109748, 4798780, 20572392, 87580308, 370706408, 1561573032, 6551178288, 27387484242, 114146434068, 474476717292, 1967642119368, 8142727008732, 33634295542968, 138696447565272, 571069686589008, 2348087834494932

Offset

1,1

Comments

Row sums of A112327.

Links

Robert Israel, Table of n, a(n) for n = 1..1656

Frank Ruskey, Average shape of binary trees, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50 (Eq. (8)).

Formula

G.f.: 4*z*(2-sqrt(1-4*z))/((1-4*z)^(3/2)*(1+sqrt(1-4*z))).

32*(2*n^2 - 9*n + 10)*a(n - 3) - 8*(2*n^2 - 14*n + 15)*a(n - 2) - 2*(2*n^2 + 3*n - 5)*a(n - 1) + n*(n - 1)*a(n) = 0. - Robert Israel, Sep 19 2019

Maple

a:=n->(n+1)*binomial(2*n+2, n+1)-3*4^n+binomial(2*n, n): seq(a(n), n=1..25);

Mathematica

a[n_]:=(n+1)*Binomial[2n+2, n+1]-3*4^n+Binomial[2n, n]; Array[a, 22] (* Stefano Spezia, Sep 20 2019 *)

Prog

(PARI) a(n) = (n+1)*binomial(2*n+2, n+1)-3*4^n+binomial(2*n, n); \\ Michel Marcus, Sep 20 2019
(Magma) [(n+1)*Binomial(2*n+2, n+1)-3*4^n+Binomial(2*n, n):n in [1..22]]; // Marius A. Burtea, Sep 20 2019

Crossrefs

Cf. A112327.

Sequence in context: A345969 A101570 A006043 * A370732 A038721 A308700

Adjacent sequences: A112325 A112326 A112327 * A112329 A112330 A112331

Keyword

nonn,easy

Author

Emeric Deutsch, Sep 04 2005

Status

approved