A261492 Number of partitions of subsets of {1,...,n}, where consecutive integers are required to be in the same part and the elements of {1, n} are required to be in the same part if they are both members of a subset.

1, 2, 4, 8, 18, 42, 102, 254, 648, 1688, 4486, 12146, 33474, 93810, 267112, 772124, 2264214, 6731254, 20275118, 61841886, 190914356, 596256556, 1883148834, 6012081046, 19395355770, 63205986042, 208003526516, 691048272152, 2317140259834, 7839542054210

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = 2 * Sum_{j=0..floor(n/2)} C(n,2*j) * A000110(j) for n>0, a(0) = 1.

Example

a(3) = 8: {}, 1, 2, 3, 12, 23, 13, 123.
a(4) = 18: {}, 1, 2, 3, 4, 12, 13, 1|3, 14, 23, 24, 2|4, 34, 123, 124, 134, 234, 1234.

Maple

with(combinat):
a:= n-> `if`(n=0, 1, 2*add(binomial(n, 2*j)*bell(j), j=0..n/2)):
seq(a(n), n=0..35);

Mathematica

a[n_] := If[n==0, 1, 2*Sum[Binomial[n, 2*j]*BellB[j], {j, 0, n/2}]]; Table[ a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 22 2017, translated from Maple *)

Crossrefs

Cf. A000110, A247100, A261134, A261041, A261489.

Sequence in context: A026699 A182780 A078678 * A027056 A024428 A330269

Adjacent sequences: A261489 A261490 A261491 * A261493 A261494 A261495

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved