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 A064299 B(n)*C(n), where B(n) are Bell numbers (A000110) and C(n) are Catalan numbers (A000108). 4
 1, 1, 4, 25, 210, 2184, 26796, 376233, 5920200, 102816714, 1947916100, 39890416020, 876478739164, 20537052247300, 510548782729680, 13407568735200525, 370553407586717490, 10742998644116921160, 325786278993936753300, 10307990595756667951830 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS From Joerg Arndt, Oct 22 2012: (Start) Number of strings of length 2*n of up to n different types t(k) of balanced parentheses, where the first appearance of type t(k) must precede the appearance of t(k+1) for all k bell(n)*ctln(n): seq(a(n), n=0..25);  # Alois P. Heinz, Mar 23 2015 MATHEMATICA a[n_] := BellB[n]*CatalanNumber[n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 25 2017 *) PROG (Sage) [bell_number(i)*catalan_number(i) for i in range(17)] # Zerinvary Lajos, Mar 14 2009 CROSSREFS Cf. A000108, A000110. Row sums of A253180. Sequence in context: A105628 A332257 A203219 * A261898 A038174 A049118 Adjacent sequences:  A064296 A064297 A064298 * A064300 A064301 A064302 KEYWORD nonn AUTHOR Karol A. Penson, Sep 05 2001 STATUS approved

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Last modified January 26 07:39 EST 2021. Contains 340434 sequences. (Running on oeis4.)