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

Author

Clark Kimberling

Keywords

• nonn
• changed

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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

Extensions

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

Edited by M. F. Hasler, Nov 08 2017