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A168606 The number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly four nonempty parts. 3
1, 4, 20, 102, 496, 2294, 10200, 44062, 186416, 776934, 3203080, 13101422, 53279136, 215749174, 870919160, 3507493182, 14101520656, 56620923014, 227128606440, 910449955342, 3647607982976, 14607859562454, 58483727432920 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Table of n, a(n) for n=4..26.

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 (10,-35,50,-24).

FORMULA

For n>=4, a(n)=(10*4^(n-4)-5*3^(n-3)+9*2^(n-4)-1)/3.

The shifted e.g.f. is (10e^(4x)-15e^(3x)+9e^(2x)-e^x)/3.

G.f. x^4(1-6x+15x^2-8x^3)/((1-x)(1-2x)(1-3x)(1-4x)).

MATHEMATICA

f6[n_] := (10 4^(n - 4) - 5 3^(n - 3) + 9 2^(n - 4) - 1)/3; Table[ f6[n], {n, 4, 28}]

CROSSREFS

The number of ways of partitioning the multiset {1, 1, 1, 2, 3, ..., n-1} into exactly two and three nonempty parts are given in A168604 and A168605 respectively.

Sequence in context: A242156 A186369 A093440 * A229135 A226198 A155485

Adjacent sequences:  A168603 A168604 A168605 * A168607 A168608 A168609

KEYWORD

nonn,easy

AUTHOR

Martin Griffiths, Dec 01 2009

EXTENSIONS

Last element of the multiset in the definition corrected by Martin Griffiths, Dec 02 2009

STATUS

approved

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Last modified February 21 01:29 EST 2019. Contains 320364 sequences. (Running on oeis4.)