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%I #7 Apr 29 2019 08:34:51
%S 0,4,49,246,834,2250,5214,10829,20696,37044,62875,102124,159834,
%T 242346,357504,514875,725984,1004564,1366821,1831714,2421250,3160794,
%U 4079394,5210121,6590424,8262500,10273679,12676824,15530746,18900634,22858500
%N Fourth left hand column of triangle A163940.
%H G. C. Greubel, <a href="/A163944/b163944.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: x*(4 +21*x -13*x^2 +x^3 +3*x^4 -x^5)/(1-x)^7.
%F a(n) = (10*n^2 +107*n^3 +61*n^4 +13*n^5 +n^6)/48.
%F a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
%F E.g.f.: (1/48)*x*(192 + 984*x + 888*x^2 + 256*x^3 + 28*x^4 + x^5)*exp(x). - _G. C. Greubel_, Aug 13 2017
%t CoefficientList[Series[x*(4 + 21*x - 13*x^2 + x^3 + 3*x^4 - x^5)/(1 - x)^7, {x, 0, 50}], x] (* _G. C. Greubel_, Aug 13 2017 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,4,49,246,834,2250,5214},40] (* _Harvey P. Dale_, Apr 29 2019 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(4 +21*x -13*x^2 +x^3 +3*x^4 -x^5)/(1-x)^7)) \\ _G. C. Greubel_, Aug 13 2017
%Y Cf. A163972.
%Y Equals the fourth left hand column of A163940.
%Y A163943 is another left hand column.
%K easy,nonn
%O 0,2
%A _Johannes W. Meijer_, Aug 13 2009
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