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Search: id:A111997
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| A111997 |
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Ninth convolution of Schroeder's (second problem) numbers A001003(n), n>=0. |
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+0
1
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| 1, 9, 63, 399, 2403, 14067, 80949, 460845, 2605590, 14666470, 82320714, 461238282, 2581644378, 14442658074, 80785970838, 451934259654, 2528977211775, 14157983986839, 79302044283297, 444448115168049, 2492468172937125
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^9.
a(n)= (9/n)*sum(binomial(n, k)*binomial(n+k+8, k-1), k=1..n) = 9*hypergeom([1-n, n+10], [2], -1), n>=1, a(0)=1.
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CROSSREFS
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Ninth column of convolution triangle A011117.
Adjacent sequences: A111994 A111995 A111996 this_sequence A111998 A111999 A112000
Sequence in context: A015669 A073378 A022733 this_sequence A016137 A037508 A037691
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 12 2005
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