A384929 a(n) = (1/2) * Sum_{k=1..n} (n+k)! / k!.

1, 9, 102, 1500, 27660, 617400, 16213680, 490069440, 16760882880, 639966096000, 26985293596800, 1245475770739200, 62451722542809600, 3380720038606310400, 196504354123773696000, 12206388145136080896000, 806977883442211633152000, 56573396890583745908736000

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..350

Formula

Recurrence: (n+1)*(3*n - 2)*a(n) = n*(15*n^2 - n - 4)*a(n-1) - 2*(n-1)*n*(2*n - 1)*(3*n + 1)*a(n-2).

a(n) = ((2*n+1)!/(n+1)! - n!)/2.

a(n) ~ 2^(2*n + 1/2) * n^n / exp(n).

Mathematica

Table[Sum[(n+k)!/k!, {k, 1, n}], {n, 1, 25}]/2

Prog

(PARI) a(n) = ((2*n+1)!/(n+1)!-n!)/2; \\ Seiichi Manyama, Sep 07 2025
(Magma) [&+[(Factorial(n+k)/Factorial(k))/2 : k in [1..n] ]: n in [1..40]]; // Vincenzo Librandi, Oct 16 2025

Crossrefs

Cf. A000142, A006963, A073013, A073014.

Sequence in context: A339643 A083452 A356244 * A367447 A081461 A231646

Adjacent sequences: A384926 A384927 A384928 * A384930 A384931 A384932

Keyword

nonn

Author

Vaclav Kotesovec, Sep 07 2025

Status

approved