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A009454
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E.g.f. sin(log(1+x)).
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4
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0, 1, -1, 1, 0, -10, 90, -730, 6160, -55900, 549900, -5864300, 67610400, -839594600, 11186357000, -159300557000, 2416003824000, -38894192662000, 662595375078000, -11911522255750000, 225382826562400000
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OFFSET
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0,6
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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a(n) = sum{k=0..n-1, (-1)^k*T(n-1, k)*cos(pi*(n-k-1)/2)}; T(n, k)=abs(A008276(n, k)). - Paul Barry, Apr 18 2005
abs(a(n)) = abs(Re(product((k+I), k=1..(n-1)))) with I^2=-1. Example: abs(a(9))=55900 and product((k+I), k=1..(9-1)) = - 55900 + 46800 I => abs(part real of "product((k+I), k=1..(9-1))") = 55900 - Yalcin (aktaryalcin(AT)msn.com), Jul 02 2005
a(n+2) = -(2n+1)*a(n+1)-(n^2+1)*a(n), a(0)=0, a(1)=1. E.g. a(8)=6160 and -13*a(7)-37*a(6)=6160 because a(7)=-730 and a(6)=90. - Remy Lachaud (pacifik31(AT)aol.com), Dec 25 2005
a(n) = sum_{k=0}^{n/2} stirling1(n,2k+1)*(-1)^k [From Vladimir Kruchinin, Aug 03 2010]
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PROG
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(Maxima(?)) sum(stirling1(n, 2*k+1)*(-1)^(k), k, 0, n/2) [From Vladimir Kruchinin, Aug 03 2010]
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CROSSREFS
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Sequence in context: A201723 A159733 A038726 * A162756 A199940 A004985
Adjacent sequences: A009451 A009452 A009453 * A009455 A009456 A009457
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin
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EXTENSIONS
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Extended with signs Mar 15 1997 by Olivier Gerard.
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STATUS
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approved
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