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A025758
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5th order Vatalan numbers (generalization of Catalan numbers).
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1
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1, 1, 11, 171, 3056, 58916, 1191376, 24896436, 532911346, 11617952106, 256966100966, 5750337968926, 129926216608236, 2959472057112396, 67877180959091156, 1566072624078270516, 36319953436423545851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
| G.f.: 5 / (4+(1-25*x)^(1/5)).
a(n) = sum(m=1..n-1, 5^(n-m)*m/n * sum(k=1..n-m, binomial(n+k-1,n-1) * sum(i=0..k, binomial(k,i) * 2^(k-i) * sum(j=0..i, binomial(j,-3*i+n-m-k+2*j) * (-1)^(j-i)*5^(j-i)*(-2)^(3*i-n+m+k-j) * binomial(i,j)))))+1. [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Feb 9 2011]
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CROSSREFS
| a(n), n >= 1, = row sums of triangle A049223.
Sequence in context: A205087 A064182 A139792 * A141955 A133243 A161355
Adjacent sequences: A025755 A025756 A025757 * A025759 A025760 A025761
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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