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A024427 S(n,1) + S(n-1,2) + +S(n-2,3) + ... + S(n+1-k,k), where k=[ (n+1)/2 ] and S(i,j) are Stirling numbers of second kind. 6
1, 1, 2, 4, 9, 22, 58, 164, 495, 1587, 5379, 19195, 71872, 281571, 1151338, 4902687, 21696505, 99598840, 473466698, 2327173489, 11810472444, 61808852380, 333170844940, 1847741027555 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..24.

FORMULA

G.f.: sum{k>=0, x^(2k)/prod[l=1..k, 1-lx]}. - Ralf Stephan, Apr 18 2004

a(n)=sum(stirling2(n-1-i,i), i=0..n-2), n>=3 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

G.f.: ((G(0) - 1)/(x-1)-x)/x^3 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.: 1/x^2/Q(0) - 1/x^2 where Q(k) = 1 - x^2/(1 - x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Apr 14 2013

MAPLE

with(combinat):seq(sum(stirling2(n-1-i, i), i=0..n-2), n=3..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008

PROG

(PARI) a(n) = sum(j=1, floor((n+1)/2), stirling(n+1-j, j, 2) ); /* Joerg Arndt, Apr 14 2013 */

CROSSREFS

Sequence in context: A192576 A059019 A121953 * A171367 A092920 A177377

Adjacent sequences:  A024424 A024425 A024426 * A024428 A024429 A024430

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 21 04:39 EDT 2013. Contains 225474 sequences.