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A052657 Expansion of e.g.f. x^2/((1-x)^2*(1+x)). 1
0, 0, 2, 6, 48, 240, 2160, 15120, 161280, 1451520, 18144000, 199584000, 2874009600, 37362124800, 610248038400, 9153720576000, 167382319104000, 2845499424768000, 57621363351552000, 1094805903679488000, 24329020081766400000, 510909421717094400000, 12364008005553684480000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Stirling transform of -(-1)^n*a(n-1) = [0, 0, 2, -6, 48, -240, ...] is A052841(n-1) = [0, 0, 2, 6, 38, 270, ...]. - Michael Somos, Mar 04 2004
LINKS
FORMULA
a(0)=0, a(1)=0, a(2)=2, n*a(n+2) = (n+2)*a(n+1) + (n^3 + 4*n^2 + 5*n + 2)*a(n).
a(n) = (2*n-1+(-1)^n)*n!/4 = n!*floor(n/2) = n!*A004526(n).
E.g.f.: x^2/((1-x)*(1-x^2)).
Sum_{n>=2} 1/a(n) = 4*CoshIntegral(1) - 4*gamma - 2*sinh(1) + 2 = 4*A099284 - 4*A001620 - 2*A073742 + 2. - Amiram Eldar, Jan 22 2023
MAPLE
spec := [S, {S=Prod(Z, Z, Sequence(Z), Sequence(Prod(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
a[n_] := Floor[n/2] * n!; Array[a, 25, 0] (* Amiram Eldar, Jan 22 2023 *)
PROG
(PARI) a(n)=if(n<0, 0, n!*polcoeff(x^2/(1-x)/(1-x^2)+x*O(x^n), n))
(PARI) a(n)=n!*(n\2); \\ Joerg Arndt, Jan 22 2023
CROSSREFS
Sequence in context: A337907 A052614 A052688 * A230714 A092143 A281027
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved

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Last modified February 23 18:28 EST 2024. Contains 370283 sequences. (Running on oeis4.)