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.

9, 26, 92, 371, 1663, 8155, 43263, 246218, 1493344, 9600683, 65133513, 464538351, 3471671717, 27109690422, 220646396816, 1867649896679, 16408260807503, 149357276866099, 1406334890073883, 13677748330883790, 137221985081833892

Offset: 0

Author

N. J. A. Sloane, Dec 30 2018

Keywords

• nonn

Comments

The initial 9 is also A020555(2).

References

• D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000110 (Bell number), A020555, A322773.

Column 2 of the array in A322765.

Programs

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);
vector(20, n, T(n-1, 2)) \\ Seiichi Manyama, Nov 21 2020

Formula

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