

A360951


Expansion of e.g.f. (cosh(x)  1)*(1 + x)*exp(x).


0



0, 0, 1, 6, 19, 50, 121, 280, 631, 1398, 3061, 6644, 14323, 30706, 65521, 139248, 294895, 622574, 1310701, 2752492, 5767147, 12058602, 25165801, 52428776, 109051879, 226492390, 469762021, 973078500, 2013265891, 4160749538, 8589934561, 17716740064, 36507221983, 75161927646, 154618822621
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OFFSET

0,4


COMMENTS

a(n) is the number of ordered set partitions of an nset into 3 sets such that the first set has an even number of elements greater than or equal to two, the second set has either one or no elements, and the third set has no restrictions.


LINKS



FORMULA

a(n) = 2^(n1) + n*2^(n2)  n  1 for n >= 2.
G.f.: x^2*(1  4*x^2 + 2*x^3)/((1  x)^2*(1  2*x)^2).  Stefano Spezia, Mar 04 2023


EXAMPLE

The 19 set partitions for n=4 are the following:
{1,2,3,4}, { }, { } (one of these);
{1,2}, { }, {3,4} (6 of these);
{1,2}, {3}, {4} (12 of these).


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



