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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.

%I A168606 #16 Feb 07 2021 07:04:59
%S A168606 1,4,20,102,496,2294,10200,44062,186416,776934,3203080,13101422,
%T A168606 53279136,215749174,870919160,3507493182,14101520656,56620923014,
%U A168606 227128606440,910449955342,3647607982976,14607859562454,58483727432920
%N A168606 The number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly four nonempty parts.
%C A168606 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.
%H A168606 G. C. Greubel, <a href="/A168606/b168606.txt">Table of n, a(n) for n = 4..1000</a>
%H A168606 M. Griffiths and I. Mezo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Griffiths/griffiths11.html">A generalization of Stirling Numbers of the Second Kind via a special multiset</a>, JIS 13 (2010) #10.2.5.
%H A168606 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F A168606 a(n) = (10*4^(n-4) - 5*3^(n-3) + 9*2^(n-4) - 1)/3.
%F A168606 The shifted e.g.f. is (10*exp(4*x) - 15*exp(3*x) + 9*exp(2*x) - exp(x))/3.
%F A168606 G.f.: x^4*(1 -6*x +15*x^2 -8*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).
%t A168606 a[n_]:= (10*4^(n-4) - 5*3^(n-3) + 9*2^(n-4) - 1)/3; Table[a[n], {n, 4, 30}]
%o A168606 (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
%o A168606 (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
%Y A168606 Cf. A168604, A168605.
%K A168606 nonn,easy
%O A168606 4,2
%A A168606 _Martin Griffiths_, Dec 01 2009
%E A168606 Last element of the multiset in the definition corrected by _Martin Griffiths_, Dec 02 2009