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A270531
a(n) = Sum_{i=1..floor(n/2)} (i*(n-i))!.
1
0, 0, 1, 2, 30, 744, 403320, 482631120, 22230943262640, 2439304469060699520, 16131709536027319923050880, 265557748777251180632423132716800, 382326737887135184960649117960539544556800, 1405822033408121123332642294795422193345577766681600
OFFSET
0,4
COMMENTS
Sum of the factorials of the products of the parts in each partition of n into two parts.
FORMULA
a(n) ~ (n^2/4)! ~ sqrt(Pi) * n^(n^2/2+1) / (2^((n^2+1)/2) * exp(n^2/4)) if n is even and a(n) ~ ((n^2-1)/4)! ~ sqrt(Pi) * n^((n^2+1)/2) / (2^(n^2/2) * exp(n^2/4)) if n is odd. - Vaclav Kotesovec, Mar 18 2016
EXAMPLE
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.
MAPLE
A270531:=n->add((i*(n-i))!, i=1..floor(n/2)): seq(A270531(n), n=0..15);
MATHEMATICA
Table[Sum[(i*(n - i))!, {i, Floor[n/2]}], {n, 0, 15}]
PROG
(PARI) a(n) = sum(k=1, n\2, (k*(n-k))!); \\ Michel Marcus, Mar 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 18 2016
STATUS
approved