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A322764 Number of set partitions of the multiset consisting of one copy each of x_1, x_2, ..., x_n, and 2 copies each of y_1 and y_2.

%I A322764 #26 Aug 06 2021 15:01:59
%S A322764 9,26,92,371,1663,8155,43263,246218,1493344,9600683,65133513,
%T A322764 464538351,3471671717,27109690422,220646396816,1867649896679,
%U A322764 16408260807503,149357276866099,1406334890073883,13677748330883790,137221985081833892
%N A322764 Number of set partitions of the multiset consisting of one copy each of x_1, x_2, ..., x_n, and 2 copies each of y_1 and y_2.
%C A322764 The initial 9 is also A020555(2).
%D A322764 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.
%H A322764 Seiichi Manyama, <a href="/A322764/b322764.txt">Table of n, a(n) for n = 0..500</a>
%F A322764 4*a(n) = 3*b(n) + 2*b(n+1) + 3*b(n+2) + 2*b(n+3) + b(n+4), where b(n) = A000110(n). - _Seiichi Manyama_, Nov 21 2020
%o A322764 (PARI) T(n, k) = if(k==0, sum(j=0, n, stirling(n, j, 2)), (T(n+2, k-1)+T(n+1, k-1)+sum(j=0, k-1, binomial(k-1, j)*T(n, j)))/2);
%o A322764 vector(20, n, T(n-1, 2)) \\ _Seiichi Manyama_, Nov 21 2020
%Y A322764 Cf. A000110 (Bell number), A020555, A322773.
%Y A322764 Column 2 of the array in A322765.
%K A322764 nonn
%O A322764 0,1
%A A322764 _N. J. A. Sloane_, Dec 30 2018