A135456 Number of surjections from an n-element set onto a seven-element set.
5040, 141120, 2328480, 29635200, 322494480, 3162075840, 28805736960, 248619571200, 2060056318320, 16540688324160, 129568848121440, 995210916336000, 7524340159588560, 56163512390086080, 414847224363337920
Offset: 7
Links
- G. C. Greubel, Table of n, a(n) for n = 7..1000
- Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).
Programs
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Mathematica
LinearRecurrence[{28, -322, 1960, -6769, 13132, -13068, 5040}, {5040, 141120, 2328480, 29635200, 322494480, 3162075840, 28805736960}, 25] (* G. C. Greubel, Oct 14 2016 *)
Formula
a(n) = 7^n -C(7,6)*6^n +C(7,5)*5^n -C(7,4)*4^n +C(7,3)*3^n -C(7,2)*2^n +C(7,1) with n>=7.
a(n) = A000771(n) * 7!. - Max Alekseyev, Nov 12 2009
G.f.: -5040*x^7/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)). - Colin Barker, Oct 25 2012
E.g.f.: (exp(x) - 1)^7. - Ilya Gutkovskiy, Jun 19 2018
Extensions
More terms from Max Alekseyev, Nov 12 2009