A336249 a(n) = (n!)^n * Sum_{k=0..n} 1 / ((k!)^n * (n-k)!).

1, 2, 7, 172, 79745, 1375363126, 1445639634946657, 136511607703654177490168, 1597074319746489837872943936307201, 3049096207067719868011671739966873049880826186, 1209808678412717193052533393657339738066086793611743000000001

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

a(n) = (n!)^n * [x^n] exp(x) * Sum_{k>=0} x^k / (k!)^n.

a(n) ~ (2*Pi)^((n-1)/2) * n^(n^2 - n/2 + 1/2) / exp(n*(n-1) - 1/12). - Vaclav Kotesovec, Jul 14 2020

Mathematica

Table[(n!)^n Sum[1/((k!)^n (n - k)!), {k, 0, n}], {n, 0, 10}]
Table[(n!)^n SeriesCoefficient[Exp[x] Sum[x^k/(k!)^n, {k, 0, n}], {x, 0, n}], {n, 0, 10}]

Prog

(PARI) a(n) = (n!)^n * sum(k=0, n, 1 / ((k!)^n * (n-k)!)); \\ Michel Marcus, Jul 14 2020

Crossrefs

Cf. A000079, A002720, A036740, A119400.

Sequence in context: A077746 A236810 A159034 * A120381 A260507 A173240

Adjacent sequences: A336246 A336247 A336248 * A336250 A336251 A336252

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 14 2020

Status

approved