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A024427
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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.
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6
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1, 1, 2, 4, 9, 22, 58, 164, 495, 1587, 5379, 19195, 71872, 281571, 1151338, 4902687, 21696505, 99598840, 473466698, 2327173489, 11810472444, 61808852380, 333170844940, 1847741027555
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..24.
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FORMULA
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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
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MAPLE
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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
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PROG
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(PARI) a(n) = sum(j=1, floor((n+1)/2), stirling(n+1-j, j, 2) ); /* Joerg Arndt, Apr 14 2013 */
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CROSSREFS
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Sequence in context: A192576 A059019 A121953 * A171367 A092920 A177377
Adjacent sequences: A024424 A024425 A024426 * A024428 A024429 A024430
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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