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A151644 Number of permutations of 4 indistinguishable copies of 1..n with exactly 6 adjacent element pairs in decreasing order. 2

%I

%S 0,0,1828,21571984,29066972368,16938467955200,6501926870387116,

%T 1978065945844840160,524378714083391626872,127734445724723139679472,

%U 29503552588857666326833140,6587452899587031432766113392,1439127765510353092008927027552,310010313330353917185364216860320

%N Number of permutations of 4 indistinguishable copies of 1..n with exactly 6 adjacent element pairs in decreasing order.

%H Andrew Howroyd, <a href="/A151644/b151644.txt">Table of n, a(n) for n = 1..200</a>

%H G. C. Greubel, <a href="/A151644/a151644.txt">Generating functions and recurrence</a>

%F From _G. C. Greubel_, Sep 12 2022: (Start)

%F a(n) = Sum_{j=0..6} (-1)^j*binomial(4*n+1, j)*binomial(10-j, 4)^n.

%F G.f., e.g.f., and recurrence are in the file "Generating functions and recurrence". (End)

%t Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[10-j, 4]^n, {j,0,6}], {n, 30}] (* _G. C. Greubel_, Sep 12 2022 *)

%o (Magma) [(&+[(-1)^j*Binomial(4*n+1, j)*Binomial(10-j, 4)^n: j in [0..6]]): n in [1..30]]; // _G. C. Greubel_, Sep 12 2022

%o (SageMath)

%o def A151644(n): return sum((-1)^j*binomial(4*n+1, j)*binomial(10-j, 4)^n for j in (0..6))

%o [A151644(n) for n in (1..30)] # _G. C. Greubel_, Sep 12 2022

%Y Column k=6 of A236463.

%K nonn

%O 1,3

%A _R. H. Hardin_, May 29 2009

%E Terms a(8) and beyond from _Andrew Howroyd_, May 06 2020

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Last modified October 4 03:29 EDT 2022. Contains 357237 sequences. (Running on oeis4.)