A299121 a(n) = Sum_{k=0..n} (k*(n-k))!.

1, 2, 3, 6, 38, 1490, 443762, 965262242, 23539096637282, 4878608938121399042, 16752209028723653862101762, 531115497554502361264846265433602, 392660148984369152453298787770243889113602, 2811644066816242246665284589590844386691155533363202

Offset: 0

Author

Vaclav Kotesovec, Feb 03 2018

Keywords

• nonn

Crossrefs

Cf. A000142, A003149, A003422.

Programs

Mathematica

Table[Sum[(k*(n-k))!, {k, 0, n}], {n, 0, 14}]

Formula

a(n) ~ sqrt(Pi) * n^(n^2/2 + 1) / (2^(n^2/2 + 1/2) * exp(n^2/4)) if n is even, and a(n) ~ sqrt(Pi) * n^(n^2/2 + 1/2) / (2^(n^2/2 - 1) * exp(n^2/4)) if n is odd.