1,3

First column in A154960. [From Mats Granvik (mats.granvik(AT)abo.fi), Jan 18 2009]

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

L. Babai and T. Lengyel, A convergence criterion for recurrent sequences with application to the partition lattice, Analysis 12 (1992), 109-119.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 316-321.

T. Lengyel, On a recurrence involving Stirling numbers, Europ. J. Combin., 5 (1984), 313-321.

M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132.

L. Babai and T. Lengyel, A convergence criterion for recurrent sequences with application to the partition lattice, Analysis 12 (1992), 109-119. [Bad link]

S. R. Finch, Lengyel's Constant

T. Prellberg, On the asymptotic analysis of a class of linear recurrences (slides).

Eric Weisstein's World of Mathematics, Lengyel's Constant

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). - Vladeta Jovovic (vladeta(AT)eunet.rs), 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).

(PARI) {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 */

Cf. A006541. Row sums of A008826.

Sequence in context: A140178 A088991 A009668 this_sequence A037964 A089285 A086906

Adjacent sequences: A005118 A005119 A005120 this_sequence A005122 A005123 A005124

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 16 2003