A168606 The number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly four nonempty parts.

1, 4, 20, 102, 496, 2294, 10200, 44062, 186416, 776934, 3203080, 13101422, 53279136, 215749174, 870919160, 3507493182, 14101520656, 56620923014, 227128606440, 910449955342, 3647607982976, 14607859562454, 58483727432920

Offset

4,2

Comments

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.

Links

G. C. Greubel, Table of n, a(n) for n = 4..1000

M. Griffiths and 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

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

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

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

Mathematica

a[n_]:= (10*4^(n-4) - 5*3^(n-3) + 9*2^(n-4) - 1)/3; Table[a[n], {n, 4, 30}]

Prog

(Sage) [(10*4^(n-4) -5*3^(n-3) +9*2^(n-4) -1)/3 for n in (4..30)] # G. C. Greubel, Feb 07 2021
(Magma) [(10*4^(n-4) -5*3^(n-3) +9*2^(n-4) -1)/3: n in [4..30]]; // G. C. Greubel, Feb 07 2021

Crossrefs

Cf. A168604, A168605.

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