A034267 a(n) = f(n,n) where f is given in A034261.

0, 1, 7, 39, 196, 930, 4257, 19019, 83512, 361998, 1553630, 6615686, 27992472, 117823940, 493768485, 2061580275, 8580127920, 35611376790, 147447066690, 609200868210, 2512267906200, 10342848445020, 42516521451690, 174535009040574, 715599131576976, 2930673247541900

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• changed

Crossrefs

Cf. A034261.

Programs

Maple

A034261 := proc(n, k) binomial(n+k, k+1)*(n*k+n+1)/(k+2); end;
seq( A034261(n,n),n=0..40) ; # R. J. Mathar, Feb 10 2025

Mathematica

a[n_] := Binomial[2*n, n+1]*(n^2 + n + 1)/(n + 2); Array[a, 25, 0] (* Amiram Eldar, Sep 04 2025 *)

Formula

Conjecture D-finite with recurrence -(n+2)*(11*n-7)*a(n) + 2*(23*n^2+44*n+30)*a(n-1) - 4*(n+5)*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 10 2025

From Amiram Eldar, Sep 04 2025: (Start)

a(n) = binomial(2*n, n+1)*(n^2+n+1)/(n+2);

a(n) ~ 2^(2*n) * sqrt(n/Pi). (End)

Extensions

Corrected and extended by N. J. A. Sloane, Apr 21 2000