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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 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 Cf. A024427, A097341, A097342. Sequence in context: A249560 A121953 A024427 * A092920 A177377 A321994 Adjacent sequences: A171364 A171365 A171366 * A171368 A171369 A171370 KEYWORD easy,nonn AUTHOR Paul Barry, Dec 06 2009 STATUS approved

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