A144896
Third column of triangle A134134 (S2'(2)= S1hat(2)).
Original entry on oeis.org
1, 2, 10, 44, 228, 1272, 8760, 63936, 547776, 5145984, 54233280, 624291840, 7879472640, 107423677440, 1579212910080, 24832164556800, 416273901926400, 7403098797158400, 139238590721126400, 2760253302701260800, 57522218527420416000, 1256931901812400128000
Offset: 0
A270531
a(n) = Sum_{i=1..floor(n/2)} (i*(n-i))!.
Original entry on oeis.org
0, 0, 1, 2, 30, 744, 403320, 482631120, 22230943262640, 2439304469060699520, 16131709536027319923050880, 265557748777251180632423132716800, 382326737887135184960649117960539544556800, 1405822033408121123332642294795422193345577766681600
Offset: 0
a(4)=30; There are 2 partitions of 4 into two parts: (3,1) and (2,2). The sum of the factorials of the products of the parts in each partition is: (3*1)! + (2*2)! = 3! + 4! = 6 + 24 = 30.
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A270531:=n->add((i*(n-i))!, i=1..floor(n/2)): seq(A270531(n), n=0..15);
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Table[Sum[(i*(n - i))!, {i, Floor[n/2]}], {n, 0, 15}]
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a(n) = sum(k=1, n\2, (k*(n-k))!); \\ Michel Marcus, Mar 22 2016
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