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A124426 Product of two successive Bell numbers. 1
1, 2, 10, 75, 780, 10556, 178031, 3630780, 87548580, 2452523325, 78697155750, 2859220516290, 116482516809889, 5277304280371714, 264005848594606490, 14493602135008296115, 868435614538568029188, 56520205738693680322836 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of partitions of the set {1,2,...,2n+1} having no blocks that contain both odd and even entries. Example: a(2)=10 because we have 135|24, 15|24|3, 1|24|35, 135|2|4, 15|2|3|4, 1|2|35|4, 13|24|5, 1|24|3|5, 13|2|4|5 and 1|2|3|4|5. a(n)=A124419(2n+1)=A124418(2n+1,0).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..324

FORMULA

a(n)=B(n)B(n+1), where B(q) are the Bell numbers (A000110), i.e., B(n)=Sum(S2(n,k),k=1..n), S2(n,k) being the Stirling numbers of the 2nd kind (A008277).

MAPLE

with(combinat): seq(bell(n)*bell(n+1), n=0..19);

MATHEMATICA

Times@@@Partition[BellB[Range[0, 20]], 2, 1] (* Harvey P. Dale, Oct 07 2018 *)

CROSSREFS

Cf. A000110, A008277, A124418, A124419.

Sequence in context: A184356 A292631 A295098 * A321394 A320956 A066223

Adjacent sequences:  A124423 A124424 A124425 * A124427 A124428 A124429

KEYWORD

nonn

AUTHOR

Emeric Deutsch and Paul D. Hanna, Nov 03 2006

STATUS

approved

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Last modified January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)