A083410 a(n) = A083385(n)/n.

1, 4, 22, 154, 1306, 12994, 148282, 1908274, 27333706, 431220034, 7428550042, 138737478994, 2792050329706, 60231133487074, 1386484468239802, 33921605427779314, 878976357571495306, 24046780495646314114, 692622345890928153562, 20950628198687114521234, 663992311200423614606506

Offset

1,2

Comments

From Michael Somos, Mar 04 2004: (Start)

Stirling transform of A052849(n+1)=[4,12,48,240,...] is 4*a(n)=[4,16,88,616,...].

Stirling transform of A001710(n+1)=[1,3,12,160,...] is a(n)=[1,4,22,154,...].

Stirling transform of A001563(n+1)=[4,18,96,600,...] is a(n+1)=[4,22,154,...]. (End)

Links

Table of n, a(n) for n=1..21.

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, arXiv:math/0307064 [math.CO], 2003; Order 21 (2004), 83-89.

Formula

E.g.f.: (1/(2-exp(x))^2-1)/2. - Michael Somos, Mar 04 2004

G.f.: 1/Q(0), where Q(k) = 1 - x*(3*k+4) - 2*x^2*(k+1)*(k+3)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 03 2013

a(n) ~ n! * n / (8 * (log(2))^(n+2)). - Vaclav Kotesovec, Jul 01 2018

Mathematica

a[n_] := (-1)^n (PolyLog[-n - 1, 2] - PolyLog[-n, 2])/8;
Array[a, 21] (* Jean-François Alcover, Sep 10 2018, from A005649 *)

Prog

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

Crossrefs

A005649(n)=2*a(n), if n>0.

Pairwise sums of A091346.

Sequence in context: A000307 A294346 A049376 * A295553 A302548 A052772

Adjacent sequences: A083407 A083408 A083409 * A083411 A083412 A083413

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2003

Status

approved