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A171367 Antidiagonal sums of triangle of Stirling numbers of 2nd kind A048993. 11
1, 0, 1, 1, 2, 4, 9, 22, 58, 164, 495, 1587, 5379, 19195, 71872, 281571, 1151338, 4902687, 21696505, 99598840, 473466698, 2327173489, 11810472444, 61808852380, 333170844940, 1847741027555, 10532499571707, 61649191750137, 370208647200165, 2278936037262610, 14369780182166215 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A249560 A121953 A024427 * A092920 A177377 A321994
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 06 2009
STATUS
approved

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Last modified May 20 02:53 EDT 2024. Contains 372703 sequences. (Running on oeis4.)