0,2

Bessel polynomial y_n(1).

Numerator of (n+1)-th convergent to 1+tanh(1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 20 2002

Number of partitions of {1,..,k}, n<=k<=2n, into n blocks with no more than 2 elements per block. Number of ways to use the elements of {1,..,k}, n<=k<=2n, once each to form a collection of n sets, each having 1 or 2 elements. - Bob Proctor, Apr 18 2005, Jun 26 2006

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.

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

P. Blasiak, A. Horzela, K. A. Penson, G.H.E. Duchamp and A. I. Solomon, Boson normal ordering via substitutions and Sheffer-type polynomials

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Index entries for sequences related to Bessel functions or polynomials

Index entries for related partition-counting sequences

E.g.f. exp(1-sqrt(1-2*x))/sqrt(1-2*x); E.g.f. if offset 1: exp(1-sqrt(1-2*x))-1.

A001515 := proc(n) option remember; if n=0 then 1 elif n=1 then 2 else (2*n-1)*A001515(n-1)+A001515(n-2); fi; end;

bessel := proc(n, x) add(binomial(n+k, 2*k)*(2*k)!*x^k/(k!*2^k), k=0..n); end;

Row sums of Bessel triangle A001497 as well as of A001498. Cf. A000806, A001517.

a(n) = A105749(n)/n!.

Partial sums: A105748.

Replace "sets" by "lists" in comment: A001517.

Adjacent sequences: A001512 A001513 A001514 this_sequence A001516 A001517 A001518

Sequence in context: A072597 A125515 A135920 this_sequence A083659 A036247 A107877

nonn,easy,nice

njas