

A115626


Number of nonsquashing partitions of {1,...,n}.


2



1, 1, 2, 4, 14, 26, 107, 190, 1234, 2182, 9947, 17414, 126953, 228398, 1039404, 1857419, 19047146, 35215110, 168364007, 307674658, 2378963269, 4429446046, 20237375204, 37371654467, 410117798653, 776233491226, 3797821367602
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OFFSET

0,3


COMMENTS

A "nonsquashing" partition of n is one where n=p_1+p_2+...+p_k with 1 <= p_1 <= p_2 <= ... <= p_k and p_1 + p_2 + ... + p_i <= p_{i+1} for all 1 <= i < k.


LINKS

Table of n, a(n) for n=0..26.
N. J. A. Sloane and J. A. Sellers, On nonsquashing partitions, arXiv:math/0312418 [math.CO], 2003.
N. J. A. Sloane and J. A. Sellers, On nonsquashing partitions, Discrete Math., 294 (2005), 259274.


FORMULA

a(n) = Sum_{i = 0..ceiling(n/2)1} (binomial(n, i)*a(i)) + [if n is even] binomial(n, n/2)*(a(n/2)1/2).


MATHEMATICA

a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n, i]*a[i], {i, 0, Ceiling[ n/2]  1}] + If[EvenQ[n], Binomial[n, n/2] (a[n/2]  1/2), 0];
Table[a[n], {n, 0, 26}] (* JeanFrançois Alcover, Oct 10 2018 *)


CROSSREFS

Cf. A018819, A115625.
Sequence in context: A050564 A047830 A036051 * A116021 A288154 A283353
Adjacent sequences: A115623 A115624 A115625 * A115627 A115628 A115629


KEYWORD

nonn


AUTHOR

Christian G. Bower, Jan 26 2006


STATUS

approved



