%I #16 Jan 25 2022 08:50:03
%S 2,48,642,6040,44130,264936,1356194,6077196,24314490,88206140,
%T 293744154,907129236,2619716554,7125357540,18363363690,45076309166,
%U 105864434424,238815143406,519252051080,1091481669390,2224042468032,4403475647758,8489857618992,15969368635950
%N Number of integer sequences of length n+1 with sum zero and sum of absolute values 16.
%H T. D. Noe, <a href="/A157057/b157057.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F a(n) = T(n,8); 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 + 7*x + 49*x^2 + 147*x^3 + 441*x^4 + 735*x^5 + 1225*x^6 + 1225*x^7 + 1225*x^8 + 735*x^9 + 441*x^10 + 147*x^11 + 49*x^12 + 7*x^13 + x^14)/(1-x)^17. - _Colin Barker_, Jan 25 2013
%F a(n) = (12870/16!)*n*(n+1)*(203212800 + 349090560*n + 487608192*n^2 + 296058000*n^3 + 196660016*n^4 + 61391512*n^5 + 25601072*n^6 + 4564385*n^7 + 1344383*n^8 + 138621*n^9 + 30835*n^10 + 1715*n^11 + 301*n^12 + 7*n^13 + n^14). - _G. C. Greubel_, Jan 24 2022
%t Table[(12870/16!)*n*(n+1)*(203212800 +349090560*n +487608192*n^2 +296058000*n^3 +196660016*n^4 +61391512*n^5 +25601072*n^6 +4564385*n^7 + 1344383*n^8 + 138621*n^9 +30835*n^10 +1715*n^11 +301*n^12 +7*n^13 +n^14), {n, 50}] (* _G. C. Greubel_, Jan 24 2022 *)
%o (Sage) [(12870/factorial(16))*n*(n+1)*(203212800 +349090560*n +487608192*n^2 +296058000*n^3 +196660016*n^4 +61391512*n^5 +25601072*n^6 +4564385*n^7 + 1344383*n^8 + 138621*n^9 +30835*n^10 +1715*n^11 +301*n^12 +7*n^13 +n^14) for n in (1..50)] # _G. C. Greubel_, Jan 24 2022
%Y Cf. A103881, A156554.
%K nonn,easy
%O 1,1
%A _R. H. Hardin_, Feb 22 2009