login
The OEIS is supported by
the many generous donors to the OEIS Foundation
.
Hints
(Greetings from
The On-Line Encyclopedia of Integer Sequences
!)
A295610
a(n) = Sum_{k=0..n} (n!/(n - k)!)^k.
1
1, 2, 7, 256, 345749, 25090776406, 139507578065088907, 82622801516492599819822772, 6985137485409222182920705065038896201, 109110989095384931538566720095053550173384985449034, 395940975233113726268241745444050219538058574725338743701918216111
(
list
;
graph
;
refs
;
listen
;
history
;
text
;
internal format
)
OFFSET
0,2
LINKS
Seiichi Manyama,
Table of n, a(n) for n = 0..30
Eric Weisstein's World of Mathematics,
Binomial Sums
FORMULA
a(n) = Sum_{k=0..n}
A219206
(n,k)*
A036740
(k).
a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n^2 + n/2) / exp(n^2 - 1/12). -
Vaclav Kotesovec
, Nov 25 2017
MATHEMATICA
Table[Sum[(n!/(n - k)!)^k, {k, 0, n}], {n, 0, 10}]
Table[Sum[(Gamma[n + 1]/Gamma[k + 1])^(n - k), {k, 0, n}], {n, 0, 10}]
Table[Sum[(Binomial[n, k] k!)^k, {k, 0, n}], {n, 0, 10}]
PROG
(PARI) a(n) = sum(k=0, n, (n!/(n - k)!)^k); \\
Michel Marcus
, Nov 25 2017
CROSSREFS
Cf.
A000522
,
A006040
,
A036740
,
A217284
,
A219206
.
Sequence in context:
A088106
A343928
A294827
*
A329967
A012942
A208018
Adjacent sequences:
A295607
A295608
A295609
*
A295611
A295612
A295613
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy
, Nov 24 2017
STATUS
approved
Lookup
|
Welcome
|
Wiki
|
Register
|
Music
|
Plot 2
|
Demos
|
Index
|
Browse
|
More
|
WebCam
Contribute new seq. or comment
|
Format
|
Style Sheet
|
Transforms
|
Superseeker
|
Recents
The OEIS Community
| Maintained by
The OEIS Foundation Inc.
License Agreements, Terms of Use, Privacy Policy.
.
Last modified April 24 14:32 EDT 2024. Contains 371960 sequences. (Running on oeis4.)