cp's OEIS Frontend

A157055 Number of integer sequences of length n+1 with sum zero and sum of absolute values 12.

%I A157055 #22 Oct 05 2024 16:30:17
%S A157055 2,36,362,2570,14240,65226,256508,889716,2777370,7925720,20934474,
%T A157055 51697802,120353324,265953170,561075720,1135620536,2214405618,
%U A157055 4175000796,7634582090,13577591370,23539760552,39868752506,66087441092,107392877100,171332460650,268708978512
%N A157055 Number of integer sequences of length n+1 with sum zero and sum of absolute values 12.
%H A157055 T. D. Noe, <a href="/A157055/b157055.txt">Table of n, a(n) for n = 1..1000</a>
%H A157055 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A157055 a(n) = T(n,6) where T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
%F A157055 G.f.: 2*x*(1 +5*x +25*x^2 +50*x^3 +100*x^4 +100*x^5 +100*x^6 +50*x^7 +25*x^8 +5*x^9 +x^10)/(1-x)^13. - _Colin Barker_, Jan 25 2013
%F A157055 From _G. C. Greubel_, Jan 24 2022: (Start)
%F A157055 a(n) = n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400.
%F A157055 E.g.f.: (x/518400)*(1036800 +8294400*x +22464000*x^2 +28728000*x^3 +20131200*x^4 +8369280*x^5 +2154240*x^6 +349200*x^7 +35400*x^8 +2160*x^9 +72*x^10 +x^11)*exp(x). (End)
%t A157055 Table[n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400, {n, 50}] (* _G. C. Greubel_, Jan 24 2022 *)
%o A157055 (Sage) [n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400 for n in (1..50)] # _G. C. Greubel_, Jan 24 2022
%Y A157055 Column k=6 of A103881.
%Y A157055 Cf. A156554.
%K A157055 nonn,easy
%O A157055 1,1
%A A157055 _R. H. Hardin_, Feb 22 2009