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A360951 Expansion of e.g.f. (cosh(x) - 1)*(1 + x)*exp(x). 0

%I #19 Mar 25 2023 14:59:12

%S 0,0,1,6,19,50,121,280,631,1398,3061,6644,14323,30706,65521,139248,

%T 294895,622574,1310701,2752492,5767147,12058602,25165801,52428776,

%U 109051879,226492390,469762021,973078500,2013265891,4160749538,8589934561,17716740064,36507221983,75161927646,154618822621

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

%C 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.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).

%F a(n) = 2^(n-1) + n*2^(n-2) - n - 1 for n >= 2.

%F G.f.: x^2*(1 - 4*x^2 + 2*x^3)/((1 - x)^2*(1 - 2*x)^2). - _Stefano Spezia_, Mar 04 2023

%F a(n) = (n + 2)*2^(n-2) - n - 1 = A129953(n) - n - 1 for n >= 2. - _Stefano Spezia_, Mar 05 2023

%e The 19 set partitions for n=4 are the following:

%e {1,2,3,4}, { }, { } (one of these);

%e {1,2}, { }, {3,4} (6 of these);

%e {1,2}, {3}, {4} (12 of these).

%Y Cf. A129953.

%K nonn,easy

%O 0,4

%A _Enrique Navarrete_, Feb 26 2023

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Last modified May 21 15:14 EDT 2024. Contains 372738 sequences. (Running on oeis4.)