The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A330497 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A330497

a(n) = n! * Sum_{k=0..n} (-1)^k * binomial(n,k) * n^(n - k) / k!.
(history; published version)

#19 by Charles R Greathouse IV at Thu Sep 08 08:46:24 EDT 2022

PROG

(MAGMAMagma) [Factorial(n)*&+[(-1)^k*Binomial(n, k)*n^(n-k)/Factorial(k):k in [0..n]]:n in [0..15]]; // Marius A. Burtea, Dec 18 2019

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#18 by Vaclav Kotesovec at Fri Dec 20 03:32:29 EST 2019

STATUS

proposed

approved

#17 by Vaclav Kotesovec at Wed Dec 18 13:39:41 EST 2019

STATUS

editing

proposed

#16 by Vaclav Kotesovec at Wed Dec 18 13:39:20 EST 2019

FORMULA

a(n) ~ sqrt(2*Pi) * BesselJ(0,2) * n^(2*n + 1/2) / exp(n). - Vaclav Kotesovec, Dec 18 2019

STATUS

proposed

editing

#15 by Marius A. Burtea at Wed Dec 18 12:53:46 EST 2019

STATUS

editing

proposed

#14 by Marius A. Burtea at Wed Dec 18 12:52:25 EST 2019

PROG

(MAGMA) [Factorial(n)*&+[(-1)^k*Binomial(n, k)*n^(n-k)/Factorial(k):k in [0..n]]:n in [0..15]]; // Marius A. Burtea, Dec 18 2019

STATUS

proposed

editing

#13 by Ilya Gutkovskiy at Wed Dec 18 12:10:41 EST 2019

STATUS

editing

proposed

#12 by Ilya Gutkovskiy at Wed Dec 18 11:51:59 EST 2019

NAME

allocated for Ilya Gutkovskiy

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

DATA

1, 0, 1, 26, 1089, 70124, 6495985, 821315214, 136115947009, 28651724077976, 7470040450004001, 2363470644596843330, 892244303052345224641, 396227360441775922668036, 204487588996059177697597969, 121370399839482643287189048374

OFFSET

0,4

FORMULA

a(n) = n! * [x^n] exp(-x/(1 - n*x)) / (1 - n*x).

a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k)^2 * n^k * k!.

MATHEMATICA

Join[{1}, Table[n! Sum[(-1)^k Binomial[n, k] n^(n - k)/k!, {k, 0, n}], {n, 1, 15}]]

Join[{1}, Table[n^n n! LaguerreL[n, 1/n], {n, 1, 15}]]

Table[n! SeriesCoefficient[Exp[-x/(1 - n x)]/(1 - n x), {x, 0, n}], {n, 0, 15}]

CROSSREFS

Cf. A009940, A025166, A061711, A277423, A307885, A318224, A319392, A330260.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Dec 18 2019

STATUS

approved

editing

#11 by Ilya Gutkovskiy at Wed Dec 18 11:51:59 EST 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#10 by Alois P. Heinz at Wed Dec 18 09:07:02 EST 2019

STATUS

reviewed

approved