A034272 - OEIS

%I #16 Sep 04 2025 01:56:09

%S 0,1,17,154,1066,6370,34748,178296,875976,4167669,19348175,88112310,

%T 395137470,1749894510,7669512840,33323053200,143720109360,

%U 615950596170,2625443201394,11137650267156,47051359045460,198038873490436,830820684414952,3475320352223440,14499176256634160

%N a(n) = f(n,n+5) where f is given in A034261.

%F From _Amiram Eldar_, Sep 04 2025: (Start)

%F a(n) = binomial(2*n+5, n+6)*(n^2+6*n+1)/(n+7);

%F a(n) ~ 2^(2*n+5) * sqrt(n/Pi). (End)

%t a[n_] := Binomial[2*n + 5, n + 6]*(n^2 + 6*n + 1)/(n + 7); Array[a, 25, 0] (* _Amiram Eldar_, Sep 04 2025 *)

%Y Cf. A034261.

%K nonn

%O 0,3

%A _Clark Kimberling_

%E Corrected and extended by _N. J. A. Sloane_, Apr 21 2000