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%I #13 Apr 17 2022 09:23:29
%S 0,0,0,8,48,368,3408,36848,454608,6294128,96556368,1624775408,
%T 29744591568,588384837488,12503968334928,284065406275568,
%U 6869235761650128,176150548586638448,4774198652678411088
%N a(n) is the number of ordered partitions of {1, 1, 1, 1, 2, 3, ..., n-3}.
%C a(n) is T_4(n) in the Griffiths and Mezo reference. - _G. C. Greubel_, Apr 15 2022
%H G. C. Greubel, <a href="/A172111/b172111.txt">Table of n, a(n) for n = 1..400</a>
%H 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.
%F a(n) = Sum_{m=1..n} Sum_{j=0..m} binomial(m,j)*binomial(j+3,4)*(-1)^(m-j)*j^(n-4), for n>=4, with a(n) = 0 for n < 4.
%F a(n) ~ n! / (48 * log(2)^(n+1)). - _Vaclav Kotesovec_, Apr 15 2022
%t f[r_, n_]:= If[n<4, 0, Sum[Sum[Binomial[m,l]Binomial[l+r-1,r](-1)^(m-l)l^(n-r), {l,m}], {m, n}]]; Table[f[4, n], {n,25}]
%o (Magma) [0,0,0] cat [(&+[ (&+[Binomial(k,j)*Binomial(j+3,4)*(-1)^(k-j)*j^(n-4): j in [0..k]]): k in [1..n]]): n in [4..25]]; // _G. C. Greubel_, Apr 15 2022
%o (Sage) [0,0,0]+[sum(sum(binomial(k,j)*binomial(j+3,4)*(-1)^(k+j)*j^(n-4) for j in (0..k)) for k in (1..n)) for n in (4..25)] # _G. C. Greubel_, Apr 15 2022
%Y This gives the row sums of A172108.
%Y Cf. A172109, A172110.
%K nonn
%O 1,4
%A _Martin Griffiths_, Jan 25 2010
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