A144513 a(n) = Sum_{k=0..n} (n+k+2)!/((n-k)!*k!*2^k).

2, 18, 162, 1670, 19980, 274932, 4296278, 75324762, 1466031690, 31386435410, 733391707752, 18578222154648, 507246285802802, 14851746921266010, 464244744007818090, 15431886798641124662, 543593886328031841828, 20228083875146926867932, 792934721766833544369830

Offset: 0

Author

N. J. A. Sloane, Dec 16 2008

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..402

Crossrefs

Equals 2*A001514 (with a different offset).

Cf. A001515, A144498, A144514.

Programs

Maple

f2:=proc(n) local k; add((n+k+2)!/((n-k)!*k!*2^k),k=0..n); end; [seq(f2(n),n=0..50)];

PARI

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

Formula

n^2*a(n) = (2*n+1)*(n^2+n+1)*a(n-1) + (n+1)^2*a(n-2). - Seiichi Manyama, Apr 07 2019