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%I #14 Jan 24 2022 07:06:42
%S 2,30,252,1500,7002,27174,91112,271224,731502,1815506,4197468,9129276,
%T 18827718,37060506,70006512,127485584,224676522,384468534,640622012,
%U 1041949020,1657762722,2584888350,3956576472,5953712520,8818775030,12873059082,18537751260
%N Number of integer sequences of length n+1 with sum zero and sum of absolute values 10.
%H T. D. Noe, <a href="/A157054/b157054.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F a(n) = T(n,5); T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
%F G.f.: 2*x*(1+4*x+16*x^2+24*x^3+36*x^4+24*x^5+16*x^6+4*x^7+x^8)/(1-x)^11. - _Colin Barker_, Mar 17 2012
%F From _G. C. Greubel_, Jan 23 2022: (Start)
%F a(n) = n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400.
%F E.g.f.: (x/14400)*(28800 +187200*x +403200*x^2 +398400*x^3 +207840*x^4 +61200*x^5 +10400*x^6 +1000*x^7 +50*x^8 +x^9)*exp(x). (End)
%t Table[n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400, {n,50}] (* _G. C. Greubel_, Jan 23 2022 *)
%o (Sage) [n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400 for n in (1..50)] # _G. C. Greubel_, Jan 23 2022
%Y Cf. A103881, A156554.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 22 2009
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