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!)
A052612 E.g.f. x*(2+x)/(1-x^2). 3
0, 2, 2, 12, 24, 240, 720, 10080, 40320, 725760, 3628800, 79833600, 479001600, 12454041600, 87178291200, 2615348736000, 20922789888000, 711374856192000, 6402373705728000, 243290200817664000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Stirling transform of (-1)^n*a(n-1)=[0,2,-2,12,-24,...] is A052856(n-1)=[0,2,4,14,76,...]. - Michael Somos, Mar 04 2004

LINKS

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 557

FORMULA

Recurrence: {a(0)=0, a(1)=2, a(2)=2, (-2-n^2-3*n)*a(n)+a(n+2)=0}.

Sum(1/2*(2+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^2))*n!.

E.g.f.: x(x+2)/(1-x^2). a(2n+1)=2(2n+1)!. a(2n)=(2n)!, if n>0.

n! if n is even, 2n! otherwise. a(n) = n!*A000034(n).

a(n) = n! / gcd(n, T(n)) where T(n) is the n-th triangular number. - Andrew S. Plewe, Jan 09 2006

MAPLE

spec := [S, {S=Prod(Z, Union(Sequence(Z), Sequence(Prod(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

MATHEMATICA

With[{nn=20}, CoefficientList[Series[x (2+x)/(1-x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jun 10 2018 *)

PROG

(PARI) a(n)=if(n<0, 0, n!*polcoeff((x^2+2*x)/(1-x^2)+x*O(x^n), n))

(PARI) a(n)=if(n<1, 0, n!*(n%2+1))

(PARI) a(n)= n! / gcd(n, n * (n + 1)) / 2) \\ Andrew S. Plewe

CROSSREFS

Sequence in context: A122007 A137782 A131384 * A287951 A287629 A324919

Adjacent sequences:  A052609 A052610 A052611 * A052613 A052614 A052615

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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 July 31 08:06 EDT 2021. Contains 346369 sequences. (Running on oeis4.)