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A042984 Number of n-dimensional partitions of 6.

%I A042984 #36 Sep 08 2022 08:44:55
%S A042984 1,11,48,140,326,657,1197,2024,3231,4927,7238,10308,14300,19397,25803,
%T A042984 33744,43469,55251,69388,86204,106050,129305,156377,187704,223755,
%U A042984 265031,312066,365428,425720,493581,569687,654752,749529,854811,971432
%N A042984 Number of n-dimensional partitions of 6.
%D A042984 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190.
%H A042984 Vincenzo Librandi, <a href="/A042984/b042984.txt">Table of n, a(n) for n = 0..1000</a>
%H A042984 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A042984 a(n) = A008780(n) - binomial(n, 4) - binomial(n, 3).
%F A042984 G.f.: (x^4 - 3*x^3 - 3*x^2 + 5*x + 1)/(x-1)^6. - _Colin Barker_, Jul 22 2012
%F A042984 a(n) = (n+1)*(n+4)*(n^3 + 40*n^2 + 61*n + 30)/120. - _Robert Israel_, Jul 06 2016
%p A042984 a:= n-> 1+10*n+27*binomial(n, 2)+28*binomial(n, 3)
%p A042984               +11*binomial(n, 4)+binomial(n, 5):
%p A042984 seq(a(n), n=0..34);
%t A042984 LinearRecurrence[{6,-15,20,-15,6,-1},{1,11,48,140,326,657},40] (* _Harvey P. Dale_, Jan 27 2013 *)
%t A042984 CoefficientList[Series[(x^4 -3x^3 -3x^2 +5x +1)/(x-1)^6, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 27 2013 *)
%o A042984 (Magma) [1 + 10*n + 27*Binomial(n,2) + 28*Binomial(n,3) + 11*Binomial(n,4) + Binomial(n,5): n in [0..40]]; // _Vincenzo Librandi_, Oct 27 2013
%o A042984 (PARI) my(x='x+O('x^40)); Vec((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6) \\ _G. C. Greubel_, Feb 17 2019
%o A042984 (Sage) ((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Feb 17 2019
%o A042984 (GAP) List([0..40],n->(n+1)*(n+4)*(n^3+40*n^2+61*n+30)/120); # _Muniru A Asiru_, Feb 17 2019
%Y A042984 Cf. A007326, A007327, A008780.
%K A042984 nonn,easy
%O A042984 0,2
%A A042984 _Alford Arnold_, Aug 15 1998
%E A042984 More terms from _Erich Friedman_