OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..665
P. Flajolet, Combinatorial aspects of continued fractions, Discrete Mathematics, Volume 32, Issue 2, 1980, pp. 125-161.
FORMULA
G.f.: 1/(1-x^2/(1-x/(1-x^2/(1-2x/(1-x^2/1-3x/(1-x^2/(1-4x/(1-x^2/(1-5x/(1-... (continued fraction).
G.f.: (G(0) - 1)/(x-1)/x where G(k) = 1 - x/(1-k*x)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 16 2013
G.f.: T(0)/(1-x^2), where T(k) = 1-x^3*(k+1)/(x^3*(k+1)-(1-x*(x+k))*(1-x*(x+1+k))/T(k+1) ); (continued fraction, after P. Flajolet, p. 140). - Sergei N. Gladkovskii, Oct 30 2013
G.f. (alternating signs): Sum_{k>=0} S(x,k)*x^k, where S(x,k)*exp(-x) is the inverse Mellin transform of Gamma(s)*s^k. - Benedict W. J. Irwin, Oct 14 2016
MAPLE
b:= proc(n, m) option remember; `if`(n<=m,
`if`(n=m, 1, 0), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..30); # Alois P. Heinz, May 16 2023
MATHEMATICA
Table[Sum[StirlingS2[n-k, k], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 18 2016 *)
PROG
(Maxima) makelist(sum(stirling2(n-k, k), k, 0, n), n, 0, 60); [Emanuele Munarini, Jun 01 2012]
(PARI) a(n) = sum(k=0, n, stirling(n-k, k, 2)); /* Joerg Arndt, Jan 16 2013 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 06 2009
STATUS
approved