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a(n) = Sum_{k=1..floor(n/2)} H_k * (n-k)!, where H_k = Sum_{j=1..k} 1/j.
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%I #13 Aug 15 2019 14:47:22

%S 0,1,2,9,33,167,944,6390,49450,434374,4259184,46122552,546390012,

%T 7027204428,97489431360,1450957014000,23058303178896,389666143681776,

%U 6977203291635840,131947560745672320,2627899581335038560,54977516540430772320,1205366436933694882560

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

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

%p 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

%o (PARI) a(n) = sum(k=1, n\2, sum(j=1, k, 1/j)*(n-k)!); \\ _Michel Marcus_, Aug 15 2019

%Y Cf. A001008, A002805.

%K easy,nonn

%O 1,3

%A _Leroy Quet_, Aug 09 2005

%E More terms from _Emeric Deutsch_, Feb 03 2006