A124426 Product of two successive Bell numbers.

1, 2, 10, 75, 780, 10556, 178031, 3630780, 87548580, 2452523325, 78697155750, 2859220516290, 116482516809889, 5277304280371714, 264005848594606490, 14493602135008296115, 868435614538568029188, 56520205738693680322836

Offset: 0

Author

Emeric Deutsch and Paul D. Hanna, Nov 03 2006

Keywords

• nonn

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

Crossrefs

Cf. A000110, A008277, A124418, A124419.

Programs

Magma

[&*[ Bell(n+k): k in [0..1] ]: n in [0..30]]; // Vincenzo Librandi, Apr 09 2020

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 *)

Formula

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