0,4

Equals INVERTi transform of the factorials, n starting with 0. Triangle A144108 has row sums = n! with left border = A052186. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008]

Stanley, R., Enumerative Combinatorics, Volume 1 (1986), p. 49

J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.

V. Strehl, The average number of splitters in a random permutation [Unpublished; included here with the author's permission.]

G.f.: F(x)/(1+x*F(x)), F(x) = Sum_{n >= 0} n!*x^n.

a(0)=1, a(1)=0, a(n) = (n-2)*a(n-1) + Sum_{k=0..n-1} a(k)*a(n-1-k) + Sum_{k=0..k-2} a(k)*a(n-2-k) if n>1. - Michael Somos Oct 11 2006

t1 := sum(n!*x^n, n=0..100): F := series(t1/(1+x*t1), x, 100): for i from 0 to 20 do printf(`%d, `, coeff(F, x, i)) od:# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 22 2009]

(PARI) {a(n)=if(n<0, 0, polcoeff( 1/ (x+1/sum(k=0, n, k!*x^k, x*O(x^n))), n))} /* Michael Somos Oct 11 2006 */

Cf. A006932.

Cf. A144108, A000142 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008]

Sequence in context: A133798 A100937 A048779 this_sequence A074538 A001564 A059276

Adjacent sequences: A052183 A052184 A052185 this_sequence A052187 A052188 A052189

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Feb 04 2000

Better description from James A. Sellers (sellersj(AT)math.psu.edu), Mar 13 2000