The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A357502 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A357502

a(n) = ((1 + sqrt(n))^n - (1 - sqrt(n))^n)/(2*sqrt(n)).
(history; published version)

#26 by Giovanni Resta at Fri Oct 14 16:29:47 EDT 2022

STATUS

proposed

approved

#25 by Chai Wah Wu at Fri Oct 14 11:12:33 EDT 2022

STATUS

editing

proposed

#24 by Chai Wah Wu at Fri Oct 14 11:12:29 EDT 2022

PROG

(Python)

from sympy import simplify, sqrt

def A357502(n): return simplify(((1+sqrt(n))**n-(1-sqrt(n))**n)/sqrt(n))>>1 # Chai Wah Wu, Oct 14 2022

STATUS

approved

editing

#23 by Alois P. Heinz at Mon Oct 03 12:11:52 EDT 2022

STATUS

editing

approved

#22 by Alois P. Heinz at Mon Oct 03 12:11:49 EDT 2022

DATA

1, 2, 6, 20, 80, 342, 1624, 8136, 43776, 246410, 1463264, 9033180, 58200064, 387905182, 2679200640, 19068105488, 139929124864, 1054773505170, 8167509816832, 64795371984420, 526534098026496, 4374163243287398, 37135913476691968, 321727849480560600, 2843141392983654400, 25599399412894035482

STATUS

approved

editing

#21 by Alois P. Heinz at Mon Oct 03 12:10:52 EDT 2022

STATUS

proposed

approved

#20 by Stefano Spezia at Mon Oct 03 00:18:08 EDT 2022

STATUS

editing

proposed

#19 by Stefano Spezia at Mon Oct 03 00:18:00 EDT 2022

MATHEMATICA

Simplify[Table[((1 + Sqrt[n])^n - (1 - Sqrt[n])^n)/(2*Sqrt[n]), {n, 26}]] (* Stefano Spezia, Oct 03 2022 *)

STATUS

proposed

editing

#18 by Kevin Ryde at Sun Oct 02 19:48:02 EDT 2022

STATUS

editing

proposed

Discussion

Sun Oct 02

19:48

Kevin Ryde: By which I mean, if it's interesting then make a sequence.

#17 by Kevin Ryde at Sun Oct 02 19:44:31 EDT 2022

COMMENTS

a(n)/n forms integer sequence which is not in OEIS: {1, 1, 2, 5, 16, 57, 232, 1017, 4864, 24641, 133024, 752765, 4476928, 27707513, 178613376, 1191756593, 8231124992, 58598528065, 429868937728, 3239768599221, 25073052286976, 198825601967609, 1614604933769216,...}

STATUS

proposed

editing

Discussion

Sun Oct 02

19:48

Kevin Ryde: No sequence in sequence.