A145062 Generalized Bessel numbers.

1, 1, 2, 3, 6, 12, 28, 69, 182, 497, 1399, 4028, 11852, 35626, 109494, 344338, 1108565, 3653536, 12320940, 42483305, 149640000, 537975261, 1972713660, 7374794356, 28100132482, 109117922021, 431821675389, 1741507272791

Offset

0,3

Comments

Hankel transform of a(n) is 1,1,1,... (by construction). Hankel transform of a(n+1) is A145063.

Is this the same as the sequence s(n) that can be seen in Fig. 8 of Zhang (2015), with a different offset? - N. J. A. Sloane, Jan 28 2016

Links

Table of n, a(n) for n=0..27.

Yan X Zhang, Four Variations on Graded Posets, arXiv preprint arXiv:1508.00318 [math.CO], 2015.

Formula

G.f.: 1/(1-x-x^2/(1-0x-x^2/(1-2x-x^2/(1-0x-x^2/(1-3x-x^2/...))))) (a continued fraction).

G.f.: 1/(U(0)+x^2) where U(k)= 1 - x*(k+1) - 2*x^2 - x^4/U(k+1) ; (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Oct 23 2012

Crossrefs

Cf. A006789.

Sequence in context: A273873 A337717 A003317 * A300323 A261230 A014278

Adjacent sequences: A145059 A145060 A145061 * A145063 A145064 A145065

Keyword

easy,nonn

Author

Paul Barry, Sep 30 2008

Status

approved