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

5,2

Links

Table of n, a(n) for n=5..24.

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).

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)).

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}]

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.

Sequence in context: A110252 A199394 A171470 * A055425 A016212 A037713

Adjacent sequences: A168582 A168583 A168584 * A168586 A168587 A168588

Keyword

nonn,easy

Author

Martin Griffiths, Nov 30 2009

Status

approved