OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
J. Touchard, Nombres exponentiels et nombres de Bernoulli, Canad. J. Math., 8 (1956), 305-320.
FORMULA
From Vladeta Jovovic, Sep 08 2002: (Start)
E.g.f.: exp(exp(x)+exp(-x)-2).
a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * a(n-k). - Ilya Gutkovskiy, Jan 27 2020
MAPLE
Bell := combinat:-bell:
A000807 := n -> add(binomial(2*n, k)*(-1)^k*Bell(k)*Bell(2*n-k), k = 0..2*n):
seq(A000807(n), n=0..17); # Peter Luschny, Sep 10 2017
MATHEMATICA
nn = 40; t = Range[0, nn]! CoefficientList[Series[Exp[Exp[x] + Exp[-x] - 2], {x, 0, nn}], x]; Take[t, {1, nn, 2}] (* T. D. Noe, Jun 20 2012 *)
PROG
(Python)
from sympy import binomial, bell
def a(n): return sum(binomial(2*n, k)*(-1)**k*bell(k)*bell(2*n - k) for k in range(2*n + 1))
print([a(n) for n in range(21)]) # Indranil Ghosh, Sep 11 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Sep 08 2002
STATUS
approved