A168585 Number of ways of partitioning the multiset {1,1,2,3,...,n-1} into exactly five nonempty parts.

1, 11, 90, 640, 4151, 25221, 146140, 817730, 4458201, 23835031, 125551790, 653873220, 3375658651, 17308994441, 88284419040, 448429907110, 2270331053501, 11464832543451, 57778226219890, 290711449879400

Offset: 5

Author

Martin Griffiths, Nov 30 2009

Keywords

• nonn
• easy

Links

• M. Griffiths, I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5.
• Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

Crossrefs

The number of ways of partitioning the multiset {1, 1, 2, 3, ..., n-1} into exactly two, three and four nonempty parts are given in A083329, A168583 and A168584, respectively.

Programs

Mathematica

f3[n_] := 1/24 (3 5^(n - 2) - 10 4^(n - 2) + 14 3^(n - 2) - 3 2^(n) + 7); Table[f3[n], {n, 3, 25}]

Formula

For a>=5, a(n) = (3*5^(n-2) - 10*4^(n-2) + 14*3^(n-2) - 3*2^(n) + 7)/24.

The shifted exponential generating function is (375e^(5x) - 640e^(4x) + 378e^(3x) - 96e^(2x) + 7e^x)/24.

The ordinary generating function is x^5(1-4x+10x^2)/((1-x)(1-2x)(1-3x)(1-4x)(1-5x)).