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%I #16 Jan 24 2022 07:05:20
%S 2,24,162,780,2970,9492,26474,66222,151560,322190,643632,1219374,
%T 2206932,3838590,6447660,10501172,16639974,25727292,38906870,57671880,
%U 83945862,120177024,169447302,235597650,323371100,438575202,588265524,780951962,1026829680
%N Number of integer sequences of length n+1 with sum zero and sum of absolute values 8.
%H T. D. Noe, <a href="/A157053/b157053.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = T(n,4); 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+3*x+9*x^2+9*x^3+9*x^4+3*x^5+x^6)/(1-x)^9. - _Colin Barker_, Mar 17 2012
%F a(n) = n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576. - _Bruno Berselli_, Mar 17 2012
%F E.g.f.: (x/576)*(1152 +5760*x +9216*x^2 +6432*x^3 +2208*x^4 +384*x^5 +32*x^6 +x^7)*exp(x). - _G. C. Greubel_, Jan 23 2022
%t Table[n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576, {n,50}] (* _G. C. Greubel_, Jan 23 2022 *)
%o (Sage) [n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576 for n in (1..50)] # _G. C. Greubel_, Jan 23 2022
%Y Cf. A103881, A156554.
%K nonn,easy
%O 1,1
%A _R. H. Hardin_, Feb 22 2009
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