A109719 a(n) = Sum_{k=1..floor(n/2)} H_k * (n-k)!, where H_k = Sum_{j=1..k} 1/j.

0, 1, 2, 9, 33, 167, 944, 6390, 49450, 434374, 4259184, 46122552, 546390012, 7027204428, 97489431360, 1450957014000, 23058303178896, 389666143681776, 6977203291635840, 131947560745672320, 2627899581335038560, 54977516540430772320, 1205366436933694882560

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Example

a(4) = H(1)*3! + H(2)*2! = 1*6+(3/2)*2 = 6+3 = 9.

Maple

H:=k->sum(1/j, j=1..k): a:=n->sum(H(k)*(n-k)!, k=1..floor(n/2)): seq(a(n), n=1..24); # Emeric Deutsch, Feb 03 2006

Prog

(PARI) a(n) = sum(k=1, n\2, sum(j=1, k, 1/j)*(n-k)!); \\ Michel Marcus, Aug 15 2019

Crossrefs

Cf. A001008, A002805.

Sequence in context: A150934 A150935 A150936 * A263685 A334443 A301868

Adjacent sequences: A109716 A109717 A109718 * A109720 A109721 A109722

Keyword

easy,nonn

Author

Leroy Quet, Aug 09 2005

Extensions

More terms from Emeric Deutsch, Feb 03 2006

Status

approved