The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A133297 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A133297

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

#52 by N. J. A. Sloane at Sat Jan 20 09:41:20 EST 2024

STATUS

proposed

approved

#51 by Robert C. Lyons at Wed Dec 20 09:33:23 EST 2023

STATUS

editing

proposed

#50 by Robert C. Lyons at Wed Dec 20 09:33:19 EST 2023

PROG

(SageSageMath)

STATUS

proposed

editing

#49 by Thomas Scheuerle at Wed Dec 20 01:29:37 EST 2023

STATUS

editing

proposed

#48 by Thomas Scheuerle at Wed Dec 20 01:29:14 EST 2023

FORMULA

From Thomas Scheuerle, Nov 17 2023: (Start)

This conjecture is true. Let "gamma" be the lower incomplete gamma function: gamma(n, x) = (n-1)! (1 - exp(-x)*Sum_{k = 0..n-1} x^k/k! ), then we can get the upper incomplete gamma function Gamma(n, x) = gamma(n, oo) - gamma(n, x). By inserting according the formula below, we will obtain the formula from Peter Bala. - _Thomas Scheuerle_, Nov 17 2023

a(n) = (-1)^(n+1)*Gamma(n, -n)/exp(n) = (-1)^(n+1)*A292977(n-1, n), for n > 0, where Gamma is the upper incomplete gamma function. - _Thomas Scheuerle_, Nov 17 2023(End)

Discussion

Wed Dec 20

01:29

Thomas Scheuerle: Yes sorry.

#47 by Sean A. Irvine at Tue Dec 19 18:04:39 EST 2023

STATUS

proposed

editing

#46 by Michel Marcus at Fri Nov 17 10:49:09 EST 2023

STATUS

editing

proposed

Discussion

Fri Nov 17

10:49

Michel Marcus: why don't you prepare your edit offline, and copy it here when ready ?

11:03

Thomas Scheuerle: It got bigger than planed. The part with the conjecture for example or the Cf was not planned.  Maybe bad management / preparation.

Tue Dec 19

18:04

Sean A. Irvine: Use the (Start) ... (End) form please.

#45 by Michel Marcus at Fri Nov 17 10:48:58 EST 2023

FORMULA

a(n) = (-1)^(n+1)*Gamma(n, -n)/exp(n) = (-1)^(n+1)*A292977(n-1, n), for n > 0. , where Gamma is the upper incomplete gamma function. - Thomas Scheuerle, Nov 17 2023

STATUS

proposed

editing

#44 by Thomas Scheuerle at Fri Nov 17 10:47:33 EST 2023

STATUS

editing

proposed

#43 by Thomas Scheuerle at Fri Nov 17 10:47:31 EST 2023

FORMULA

This conjecture is true. Let "gamma" be the lower incomplete gamma function: gamma(n, x) = (n-1)! (1 - exp(-x) *Sum_{k = 0..n-1} x^k/k! ), then we can get the upper incomplete gamma function Gamma(n, x) = gamma(n, oo) - gamma(n, x). By inserting according the formula below, we will obtain the formula from Peter Bala. - Thomas Scheuerle, Nov 17 2023

STATUS

proposed

editing