The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A107252 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A107252

a(n) = Product_{k=0..n-1} (n+k)!/(k+1)!.
(history; published version)

#21 by Charles R Greathouse IV at Thu Sep 08 08:45:18 EDT 2022

PROG

(MAGMAMagma) [1] cat [(&*[Factorial(n+k)/Factorial(k+1): k in [0..n-1]]): n in [1..10]]; // G. C. Greubel, May 21 2019

Discussion

Thu Sep 08

08:45

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

#20 by Michael De Vlieger at Tue May 31 06:50:20 EDT 2022

STATUS

proposed

approved

#19 by Michel Marcus at Tue May 31 05:10:05 EDT 2022

STATUS

editing

proposed

#18 by Michel Marcus at Tue May 31 05:09:58 EDT 2022

MATHEMATICA

Table[Product[(n+k)!/(k+1)!, {k, 0, n-1}], {n, 0, 10}] - _(* _Alexander Adamchuk_, Jul 10 2006 *)

STATUS

approved

editing

#17 by Peter Luschny at Tue May 21 02:55:40 EDT 2019

STATUS

editing

approved

#16 by Peter Luschny at Tue May 21 02:55:34 EDT 2019

FORMULA

a(n) = (G(1+2*n)*n!*((G(2+n)*Gamma(2+n))/G(3+n))^(n-1))/G(2+n)^2 , where G(x) is the Barnes G function. - Peter Luschny, May 20 2019

CROSSREFS

Cf. A000178, A001700, A005130, A009963, A110131, A112332, A107254, A000142.

#15 by G. C. Greubel at Tue May 21 02:55:23 EDT 2019

PROG

(PARI) {a(n) = prod(k=0, n-1, (n+k)!/(k+1)!)}; \\ G. C. Greubel, May 21 2019

(MAGMA) [1] cat [(&*[Factorial(n+k)/Factorial(k+1): k in [0..n-1]]): n in [1..10]]; // G. C. Greubel, May 21 2019

(Sage) [product(factorial(n+k)/factorial(k+1) for k in (0..n-1)) for n in (0..10)] # G. C. Greubel, May 21 2019

STATUS

proposed

editing

#14 by Vaclav Kotesovec at Tue May 21 02:38:48 EDT 2019

STATUS

editing

proposed

#13 by Vaclav Kotesovec at Tue May 21 02:38:38 EDT 2019

FORMULA

a(n) ~ A * 2^(2*n^2 - 7/12) * n^(n^2 - n - 5/12) / (sqrt(Pi) * exp(3*n^2/2 - n + 1/12)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, May 21 2019

STATUS

proposed

editing

#12 by Sean A. Irvine at Tue May 21 01:30:25 EDT 2019

STATUS

editing

proposed