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Fourth left hand column of triangle A163940.
4

%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