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A064299
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B(n)*C(n), where B(n) are Bell numbers (A000110) and C(n) are Catalan numbers (A000108).
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0
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1, 1, 4, 25, 210, 2184, 26796, 376233, 5920200, 102816714, 1947916100, 39890416020, 876478739164, 20537052247300, 510548782729680, 13407568735200525, 370553407586717490
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| K. A. Penson and J.-M. Sixdeniers, Integral Representations of Catalan and Related Numbers, J. Integer Sequences, 4 (2001), #01.2.5.
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FORMULA
| Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n) = int(x^n*sum(sqrt((4*k-x)/x)*Heaviside(4*k-x)/(k*k!), k = 1..infinity)/(2*Pi*exp(1)), x = 0..infinity); this representation is unique.
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PROG
| (Other) SAGE: sage: [bell_number(i)*catalan_number(i) for i in range(17)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 14 2009]
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CROSSREFS
| Cf. A000108, A000110.
Sequence in context: A005411 A105628 A203219 * A038174 A049118 A047733
Adjacent sequences: A064296 A064297 A064298 * A064300 A064301 A064302
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 05 2001
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