login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A185025 Triangular array read by rows. T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} that have exactly k 2-cycles for n >= 0 and 0 <= k <= floor(n/2). 1
1, 1, 3, 1, 18, 9, 163, 90, 3, 1950, 1100, 75, 28821, 16245, 1575, 15, 505876, 283122, 33810, 735, 10270569, 5699932, 780150, 26460, 105, 236644092, 130267440, 19615932, 884520, 8505, 6098971555, 3332614725, 538325550, 29619450, 467775, 945 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

It appears that as n gets large, row n conforms to a Poisson distribution with mean = 1/2.  In other words (as n gets large) T(n,k) approaches n^n/(2^k*k!*e^(1/2))

Note that Sum_{k=1,...floor(n/2) T(n,k)*k = A081131(n).

Column for k=0 is A089466.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

E.g.f.: exp(T(x)^2/2*(y-1))/(1 - T(x)) where T(x) is the e.g.f. for A000169.

EXAMPLE

1,

1,

3,          1,

18,         9,

163,        90,         3,

1950,       1100,       75,

28821,      16245,      1575,      15,

505876,     283122,     33810,     735,

10270569,   5699932,    780150,    26460,    105,

236644092,  130267440,  19615932,  884520,   8505,

6098971555, 3332614725, 538325550, 29619450, 467775, 945

MATHEMATICA

nn=10; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[Exp[t^2/2(y-1)]/(1-t), {x, 0, nn}], {x, y}]//Grid

CROSSREFS

Sequence in context: A071210 A051141 A068141 * A051238 A283150 A307064

Adjacent sequences:  A185022 A185023 A185024 * A185026 A185027 A185028

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Dec 24 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)