cp's OEIS Frontend

A055251 Eighth column of triangle A055249.

%I A055251 #17 Sep 20 2017 09:09:11
%S A055251 1,10,57,244,874,2772,8054,21920,56751,141326,341303,804276,1858080,
%T A055251 4223784,9474444,21018144,46195149,100734354,218190469,469866964,
%U A055251 1006759110,2147634364,4563581746,9663887808,20401343003,42949963286,90194651043,188978952404
%N A055251 Eighth column of triangle A055249.
%C A055251 A045618 Partial sums of A000337(n+4),n>=0,
%C A055251 A045889 Partial sums of A045618,
%C A055251 A034009 Partial sums of A045889,
%C A055251 (A055250 Seventh column of triangle A055249) Partial sums of A034009,
%C A055251 (A055251 Eighth column of triangle A055249) Partial sums of A055250. - Vladimir Joseph Stephan Orlovsky, Jul 09 2011
%H A055251 Colin Barker, <a href="/A055251/b055251.txt">Table of n, a(n) for n = 0..1000</a>
%H A055251 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (10,-43,104,-155,146,-85,28,-4).
%F A055251 G.f.: 1 / (((1-2*x)^2)*(1-x)^6).
%F A055251 a(n) = A055249(n+7, 7).
%F A055251 For n >= 1, a(n) = A035039(n+7) + Sum_{j=0..n-1} a(j).
%F A055251 a(n) = Sum_{k=0..n+6} Sum_{i=0..n+6} (i-k) * C(n-k+6,i+4). - _Wesley Ivan Hurt_, Sep 19 2017
%F A055251 a(n) = (1/120)*(38520 - 75*2^(9+n) + 2*(9637 + 15*2^(8+n))*n + 4285*n^2 + 525*n^3 + 35*n^4 + n^5). - _Colin Barker_, Sep 20 2017
%p A055251 a:= n-> (Matrix(8, (i,j)-> if (i=j-1) then 1 elif j=1 then [10,-43,104,-155, 146,-85,28,-4][i] else 0 fi)^(n))[1,1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Aug 05 2008
%t A055251 Table[Sum[(-1)^(n - k) k (-1)^(n - k) Binomial[n + 6, k + 6], {k, 0, n}], {n, 1, 26}] (* _Zerinvary Lajos_, Jul 08 2009 *)
%o A055251 (PARI) Vec(1 / ((1 - x)^6*(1 - 2*x)^2) + O(x^30)) \\ _Colin Barker_, Sep 20 2017
%Y A055251 Cf. A055249, A035039, partial sums of A055250.
%K A055251 easy,nonn
%O A055251 0,2
%A A055251 _Wolfdieter Lang_, May 26 2000