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proposed

a[n_] := 2*Binomial[n-1, 4] + 13*Binomial[n-1, 5] + 27*Binomial[n-1, 6] + 29*Binomial[n-1, 7] + 14*Binomial[n-1, 8];

Table[a[n], {n, 5, 50}] (* Jean-François Alcover, Nov 26 2017, after R. J. Mathar *)

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<a href="/index/Rec#order_09">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

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2, 23, 135, 561, 1870, 5328, 13476, 31020, 66132, 132275, 250679, 453609, 788580, 1323688, 2154240, 3410880, 5269422, 7962615, 11794079, 17154665, 24541506, 34580040, 48049300, 65910780, 89341200, 119769507, 158918463, 208851185, 272023016, 351339120

<a href="/index/Rec#order_09">Index to sequences with linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

G.f.: -x^5*(2+5*x+6*x^3+x^4) / ( (x-1)^9 ). - R. J. Mathar, Apr 23 2015

A235594 := proc(n)

2*binomial(n-1, 4)

+13*binomial(n-1, 5)

+27*binomial(n-1, 6)

+29*binomial(n-1, 7)

+14*binomial(n-1, 8) ;

end proc:

seq(A235594(n), n=5..50) ; # R. J. Mathar, Apr 23 2015

nonn,more,easy,changed

M. Jones, S. Kitaev, J. Remmel, Frame patterns in n-cycles, arXiv preprint arXiv:1311.3332, 2013

M. Jones, S. Kitaev, J. Remmel, <a href="http://arxiv.org/abs/1311.3332">Frame patterns in n-cycles</a>, arXiv preprint arXiv:1311.3332, 2013

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allocated for N. J. A. Sloane

Coefficient of q^4 in the polynomial NT_{n,mu}(q).

2, 23, 135, 561, 1870, 5328, 13476

5,1

See Jones et al. (2013) for precise definition.

M. Jones, S. Kitaev, J. Remmel, Frame patterns in n-cycles, arXiv preprint arXiv:1311.3332, 2013

Cf. A235593.

allocated

nonn,more

N. J. A. Sloane, Jan 13 2014

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allocated for N. J. A. Sloane

allocated

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