0,2

Exponential self-convolution of numbers of preferential arrangements.

Number of compatible bipartitional relations on a set of cardinality n. - Ralf Stephan, Apr 27 2003

Stirling transform of A052558 : 1, 1, 4, 12, 72, 360, . . . - Philippe DELEHAM, May 17 2005

With an extra 1 at the beginning, coefficients of the formal (divergent) series expansion at infinity of Sum_{k>=0} 1/binomial(x,k) = 1+1/x+2/x^2+8/x^3+... Also Sum_{k>=0} k!/x^k Product_{i=1..k-1} 1/(1- i/x) yields a generating function in 1/x - Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Nov 21 2000

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.

T. D. Noe, Table of n, a(n) for n=0..100

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 154

Foata, D. and Krattenthaler, C., Graphical Major Indices, II, Seminaire Lotharingien de Combinatoire, B34k, 16 pp., 1995.

D. Foata and D. Zeilberger, [math/9406220] The Graphical Major Index

E.g.f.: 1/(2-exp(x))^2.

a(n) = (A000670(n) + A000670(n+1)) / 2 . - Philippe DELEHAM, May 16 2005

Sum[(i + j)^n/2^(2 + i + j), {i, 0, Infinity}, {j, 0, Infinity}] [From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Dec 31 2008]

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

Cf. A000670.

2*A083410(n)=a(n), if n>0.

Pairwise sums of A052841 and also of A089677.

Adjacent sequences: A005646 A005647 A005648 this_sequence A005650 A005651 A005652

Sequence in context: A075792 A052897 A137984 this_sequence A005363 A123307 A126101

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)