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Expansion of 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)).
1

%I #26 Oct 03 2017 02:14:08

%S 1,70,3321,135450,5143341,188253030,6755426161,239789821810,

%T 8459827013781,297439462109790,10437310023978201,365844613023404970,

%U 12815338551339471421,448752409725746315350,15710645734163363925441,549958830422813492568930,19250283677858902044252261

%N Expansion of 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)).

%C Note that the denominator has 5 tetrahedral numbers: 1, 4, 10, 20, 35.

%H G. C. Greubel, <a href="/A227273/b227273.txt">Table of n, a(n) for n = 0..645</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (70,-1579,13510,-40000,28000).

%F a(n) = (2736*35^(n+4) - 23715*20^(n+4) + 80104*10^(n+4) - 121125*4^(n+4) + 62000)/1081404000.

%t CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 10 x) (1 - 20 x) (1 - 35 x)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 02 2017 *)

%o (PARI) Vec(1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)) + O(x^50)) \\ _Michel Marcus_, May 23 2014

%Y Column k=4 of A080249.

%Y Cf. A080250, A002450, A000292.

%K nonn,easy

%O 0,2

%A _Yahia Kahloune_, Jul 04 2013

%E Typo in a(7) fixed by _Colin Barker_, May 23 2014