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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n) is the number of ordered set partitions of an n-set 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^(n-1) + n*2^(n-2) - 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
a(n) = (n + 2)*2^(n-2) - n - 1 = A129953(n) - n - 1 for n >= 2. - Stefano Spezia, Mar 05 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
Cf. A129953.
Sequence in context: A269059 A324218 A229731 * A271904 A272541 A273142
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Feb 26 2023
STATUS
approved

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Last modified April 21 10:29 EDT 2024. Contains 371852 sequences. (Running on oeis4.)