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

%I A360951 #19 Mar 25 2023 14:59:12
%S A360951 0,0,1,6,19,50,121,280,631,1398,3061,6644,14323,30706,65521,139248,
%T A360951 294895,622574,1310701,2752492,5767147,12058602,25165801,52428776,
%U A360951 109051879,226492390,469762021,973078500,2013265891,4160749538,8589934561,17716740064,36507221983,75161927646,154618822621
%N A360951 Expansion of e.g.f. (cosh(x) - 1)*(1 + x)*exp(x).
%C A360951 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 A360951 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A360951 a(n) = 2^(n-1) + n*2^(n-2) - n - 1 for n >= 2.
%F A360951 G.f.: x^2*(1 - 4*x^2 + 2*x^3)/((1 - x)^2*(1 - 2*x)^2). - _Stefano Spezia_, Mar 04 2023
%F A360951 a(n) = (n + 2)*2^(n-2) - n - 1 = A129953(n) - n - 1 for n >= 2. - _Stefano Spezia_, Mar 05 2023
%e A360951 The 19 set partitions for n=4 are the following:
%e A360951   {1,2,3,4}, { }, { } (one of these);
%e A360951   {1,2}, { }, {3,4}   (6 of these);
%e A360951   {1,2}, {3}, {4}     (12 of these).
%Y A360951 Cf. A129953.
%K A360951 nonn,easy
%O A360951 0,4
%A A360951 _Enrique Navarrete_, Feb 26 2023