A368792 a(n) = (2*n-1)!! * Sum_{k=0..n} k/(2*k-1)!!.
0, 1, 5, 28, 200, 1805, 19861, 258200, 3873008, 65841145, 1250981765, 26270617076, 604224192760, 15105604819013, 407851330113365, 11827688573287600, 366658345771915616, 12099725410473215345, 423490389366562537093, 15669144406562813872460
Offset: 0
Programs
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Mathematica
Table[(2n-1)!!Sum[k/(2k-1)!!,{k,0,n}],{n,0,20}] (* Harvey P. Dale, Sep 04 2025 *) -
PARI
a001147(n) = prod(k=1, n, 2*k-1); a(n) = a001147(n)*sum(k=0, n, k/a001147(k));
Formula
a(0) = 0; a(n) = (2*n-1)*a(n-1) + n.