1,3

Stirling transform of (-1)^n*a(n-1)=[0,1,-1,5,-14,94,...] is A000629(n-2)=[0,1,2,6,26,...]. - Michael Somos Mar 04 2004

Stirling transform of a(n)=[1,1,5,14,94,...] is A052882(n)=[1,2,9,52,375,...]. - Michael Somos Mar 04 2004

a(n) is the number of n-permutations that have a cycle with length greater than n/2. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), May 28 2009]

E.g.f.: ln(1+x)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 25 2002

a(n)=a(n-1)+a(n-2)*(n-1)^2, n>1. - Michael Somos, Oct 29, 2002

b(n) = n! satisfies the above recurrence with b(1) = 1, b(2) = 2. This gives the finite continued fraction expansion a(n)/n! = 1/(1+1^2/(1+2^2/(1+3^2/(1+...+(n-1)^2/1)))). Cf. A142979. - Peter Bala (pbala(AT)toucansurf.com), Jul 17 2008

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

Cf. A000254.

Cf. A142979.

Sequence in context: A166795 A128102 A007838 this_sequence A077262 A058072 A027304

Adjacent sequences: A024164 A024165 A024166 this_sequence A024168 A024169 A024170

nonn,easy

Clark Kimberling (ck6(AT)evansville.edu)

More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 27 2002