A144514 a(n) = Sum_{k=0..n} (n+k+3)!/((n-k)!*k!*2^k).

6, 84, 1050, 13980, 205800, 3368316, 61075854, 1219445100, 26635157010, 632479986600, 16235529291696, 448220024574504, 13247429692101150, 417453231024613140, 13974133833217747650, 495278130521939366196, 18530507890959175097784, 729908595489477119015700

Offset: 0

Author

N. J. A. Sloane, Dec 16 2008

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..401

Crossrefs

Equals 6*A144506 (with a different offset).

Cf. A001515, A144498, A144513.

Programs

Maple

f3:=proc(n) local k; add((n+k+3)!/((n-k)!*k!*2^k),k=0..n); end; [seq(f3(n),n=0..50)];

Mathematica

Table[Sum[(n+k+3)!/((n-k)!k! 2^k),{k,0,n}],{n,0,20}] (* Harvey P. Dale, Jul 27 2019 *)

PARI

{a(n) = sum(k=0, n, (n+k+3)!/((n-k)!*k!*2^k))} \\ Seiichi Manyama, Apr 07 2019

Formula

a(n) ~ 2^(n + 7/2) * n^(n+3) / exp(n-1). - Vaclav Kotesovec, Apr 07 2019