The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A016853 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A016853

a(n) = (5*n)^5.
(history; published version)

#21 by Jon E. Schoenfield at Mon Dec 27 22:20:36 EST 2021

STATUS

editing

approved

#20 by Jon E. Schoenfield at Mon Dec 27 22:20:35 EST 2021

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#19 by Bruno Berselli at Tue Oct 24 09:36:01 EDT 2017

STATUS

editing

approved

#18 by Bruno Berselli at Tue Oct 24 09:35:49 EDT 2017

MATHEMATICA

(5 * Range[0, 20])^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3125, 100000, 759375, 3200000, 9765625}, 20] (* Harvey P. Dale, Jul 11 2015 *)

PROG

(MAGMA) I:=[0, 3125, 100000, 759375, 3200000, 9765625]; [n le 6 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)- 15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..25]]; // Vincenzo Librandi, Oct 24 2017

STATUS

proposed

editing

#17 by Vincenzo Librandi at Tue Oct 24 02:03:30 EDT 2017

STATUS

editing

proposed

#16 by Vincenzo Librandi at Tue Oct 24 02:03:08 EDT 2017

DATA

0, 3125, 100000, 759375, 3200000, 9765625, 24300000, 52521875, 102400000, 184528125, 312500000, 503284375, 777600000, 1160290625, 1680700000, 2373046875, 3276800000, 4437053125, 5904900000, 7737809375, 10000000000, 12762815625, 16105100000, 20113571875, 24883200000

PROG

#15 by Vincenzo Librandi at Tue Oct 24 01:57:18 EDT 2017

NAME

a(n) = (5n5*n)^5.

LINKS

Vincenzo Librandi, <a href="/A016853/b016853.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

G.f.: 3125*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^6. - Vincenzo Librandi, Oct 24 2017

MATHEMATICA

CoefficientList[Series[3125 x (1 + 26 x + 66 x^2 + 26 x^3 + x^4) / (1-x)^6, {x, 0, 33}], x] (* Vincenzo Librandi, Oct 24 2017 *)

STATUS

proposed

editing

#14 by Michel Marcus at Tue Oct 24 01:20:54 EDT 2017

STATUS

editing

proposed

#13 by Michel Marcus at Tue Oct 24 01:20:45 EDT 2017

FORMULA

a(n) = 3125*A000584(n). - Michel Marcus, Oct 24 2017

CROSSREFS

Cf. A000584.

#12 by Michel Marcus at Tue Oct 24 01:18:49 EDT 2017

NAME

a(n) = (5n)^5.

FORMULA

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), with a(0) = 0, a(1) = 3125, a(2) = 100000, a(3) = 759375, a(4) = 3200000, a(5) = 9765625, a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Harvey P. Dale, Jul 11 2015

STATUS

proposed

editing