A154960 -id:A154960 - cp's OEIS frontend

A154961 2nd column of A154960.

0, 1, 3, 25, 340, 7026, 204862, 8007602, 404077632, 25569505628, 1982619985192, 184861494417920, 20406183592852460, 2631875641089358912, 392163247878318070876, 66855512799464487146588, 12929525365915201064027856, 2815456378791384288128303192

Offset: 1

Mats Granvik, Jan 18 2009

nonn

A052882 might have similarities with this sequence because A052882 is the 2nd column in table A154921 which is similar to A154960.

Cf. A052882, A154921, A154960.

{ (matrix(30,30,i,j,(-1)^(i!=j)*stirling(i,j,2))^(-1))[,2] } \\ Max Alekseyev, Jun 17 2011

More terms from Max Alekseyev, Jun 17 2011

A005121 Number of ultradissimilarity relations on an n-set.

Original entry on oeis.org

1, 1, 4, 32, 436, 9012, 262760, 10270696, 518277560, 32795928016, 2542945605432, 237106822506952, 26173354092593696, 3375693096567983232, 502995942483693043200, 85750135569136650473360, 16583651916595710735271248, 3611157196483089769387182064, 879518067472225603327860638128

Offset: 1

N. J. A. Sloane

First column in A154960. - Mats Granvik, Jan 18 2009

Number of chains from minimum to maximum in the lattice of set partitions of {1, ..., n} ordered by refinement. - Gus Wiseman, Jul 22 2018

			From _Gus Wiseman_, Jul 22 2018: (Start)
The (3) = 4 chains from minimum to maximum in the lattice of set partitions of {1,2,3}:
  {{1},{2},{3}} < {{1,2,3}}
  {{1},{2},{3}} < {{1},{2,3}} < {{1,2,3}}
  {{1},{2},{3}} < {{2},{1,3}} < {{1,2,3}}
  {{1},{2},{3}} < {{3},{1,2}} < {{1,2,3}}
(End)

L. Babai and T. Lengyel, A convergence criterion for recurrent sequences with application to the partition lattice, Analysis 12 (1992), 109-119.
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 316-321.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 1..100
L. Babai and T. Lengyel, A convergence criterion for recurrent sequences with application to the partition lattice, Analysis 12 (1992), 109-119.
D. Barsky, J.-P. Bézivin, p-adic Properties of Lengyel's Numbers, Journal of Integer Sequences, 17 (2014), #14.7.3.
P. J. Cameron, Some treelike objects, Quart. J. Math. Oxford, 38 (1987), 155-183. See p. 170 - _N. J. A. Sloane_, Apr 18 2014
Steven R. Finch, Lengyel's Constant [Broken link]
Steven R. Finch, Lengyel's Constant [From the Wayback machine]
T. Lengyel, On a recurrence involving Stirling numbers, Europ. J. Combin., 5 (1984), 313-321.
T. Lengyel, On some 2-adic properties of a recurrence involving Stirling numbers, p-Adic Numbers Ultrametric Anal. Appl. 4, No. 3, 179-186 (2012).
F. Murtagh, Counting dendrograms: a survey, Discrete Appl. Math., 7 (1984), 191-199.
T. Prellberg, On the asymptotic analysis of a class of linear recurrences (slides).
M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132.
M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132. [Annotated scanned copy]
M. Schader, Letter to N. J. A. Sloane, Aug 25 1981.
Eric Weisstein's World of Mathematics, Lengyel's Constant

Row sums of A008826.

Cf. A000110, A000258, A002846, A006541, A006472, A213427, A265947, A317145.

a[1] = 1; a[n_] := a[n] = Sum[StirlingS2[n, k]*a[k], {k, 1, n-1}]; Array[a, 19]
(* Jean-François Alcover, Jun 24 2011, after Vladeta Jovovic *)

{a(n) = local(A); if( n<1, 0, for(k=1, n, A = truncate(A) + x*O(x^k); A = x - A + subst(A, x, exp(x + x*O(x^k)) - 1)); n! * polcoeff(A, n))} /* Michael Somos, Sep 22 2007 */

a(n) = Sum_{i=1..n-1} N_i(n), where N_k(m) = Sum_{j=k..m-1} Stirling2(m, j)*N_{k-1}(j), m=3..n, k=2..m-1; N_1(2)=N_1(3)=...=N_1(n)=1.
a(n) = Sum_{k=1..n-1} Stirling2(n, k)*a(k) [Lengyel]. - Vladeta Jovovic, Apr 16 2003
E.g.f. satisfies Z(z) = 1/2 * (Z(exp(z)-1) - z). [Lengyel]
Asymptotic growth: a(n) ~ C_L*(n!)^2*(2log(2))^(-n)*n^(-1-1/3*log(2)) (Babai and Lengyel), with C_L = 1.0986858055... = A086053 [Flajolet and Salvy].
Sum_{k>=1} a(k-1)/fallfac(n,k) = -1/n^2 + 2*Sum_{k>=1} a(k-1)/n^k, with the falling factorials fallfac(n,k) = Product_{j=0..k-1}(n-j). - Vaclav Kotesovec, Aug 04 2015

More terms from Vladeta Jovovic, Apr 16 2003

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A154961 2nd column of A154960.

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A005121 Number of ultradissimilarity relations on an n-set.

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A154959 Triangle read by rows. Signed version of A008277.

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