A034273 a(n) = binomial(2*n+6,n+7)*(n^2+7*n+1)/(n+8) = f(n,n+6) where f is given in A034261.

0, 1, 19, 186, 1365, 8540, 48348, 255816, 1289739, 6273135, 29683225, 137447310, 625482585, 2806282440, 12443418600, 54633668400, 237871030860, 1028260382994, 4417404967206, 18874729444340, 80265980340370, 339907420551336, 1434074601137640, 6030288337651760

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1655

Formula

a(n) ~ 2^(2*n+6) * sqrt(n/Pi). - Amiram Eldar, Sep 04 2025

Mathematica

f[a_, b_] := Binomial[a + b, b + 1] (a b + a + 1)/(b + 2); Array[f[#, # + 6] &, 22, 0] (* Michael De Vlieger, Nov 08 2017 *)

Prog

(PARI) A034273(n)=binomial(2*n+6, n+7)*(n^2+7*n+1)/(n+8) \\ M. F. Hasler, Nov 08 2017

Crossrefs

Cf. A034261 (main entry), A034263 - A034275 (other columns and diagonals n -> f(n,n+k)).

Sequence in context: A008419 A211866 A327848 * A193575 A161512 A162347

Adjacent sequences: A034270 A034271 A034272 * A034274 A034275 A034276

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Edited by M. F. Hasler, Nov 08 2017

Status

approved