cp's OEIS Frontend

A157058 Number of integer sequences of length n+1 with sum zero and sum of absolute values 18.

%I A157058 #14 Jan 25 2022 08:49:46
%S A157058 2,54,812,8580,70310,472626,2703512,13507416,60110030,241925530,
%T A157058 891454124,3037849828,9654482474,28818500830,81289041680,217815522736,
%U A157058 556959705302,1364497268946,3214138597460,7302195414780,16045139112002,34183012888134,70764981877592
%N A157058 Number of integer sequences of length n+1 with sum zero and sum of absolute values 18.
%H A157058 T. D. Noe, <a href="/A157058/b157058.txt">Table of n, a(n) for n = 1..1000</a>
%H A157058 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (19,-171,969,-3876,11628,-27132,50388,-75582, 92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).
%F A157058 a(n) = T(n,9); T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
%F A157058 G.f.: 2*x*(1 +8*x +64*x^2 +224*x^3 +784*x^4 +1568*x^5 +3136*x^6 +3920*x^7 +4900*x^8 +3920*x^9 +3136*x^10 +1568*x^11 +784*x^12 +224*x^13 +64*x^14 +8*x^15 +x^16)/(1-x)^19. - _Colin Barker_, Jan 25 2013
%F A157058 a(n) = (48620/18!)*n*(n+1)*(14631321600 +26760222720*n +38452817664*n^2 +25217041536*n^3 +17311651344*n^4 +5993468992*n^5 +2592460808*n^6 +533444296*n^7 +163476113*n^8 +20735776*n^9 +4812092*n^10 +370160*n^11 +67942*n^12 +2912*n^13 +436*n^14 +8*n^15 +n^16). - _G. C. Greubel_, Jan 24 2022
%t A157058 Table[(48620/18!)*n*(n+1)*(14631321600 +26760222720*n +38452817664*n^2 +25217041536*n^3 +17311651344*n^4 +5993468992*n^5 +2592460808*n^6 +533444296*n^7 +163476113*n^8 +20735776*n^9 +4812092*n^10 +370160*n^11 +67942*n^12 +2912*n^13 +436*n^14 +8*n^15 +n^16), {n,50}] (* _G. C. Greubel_, Jan 24 2022 *)
%o A157058 (Sage) [(48620/factorial(18))*n*(n+1)*(14631321600 +26760222720*n +38452817664*n^2 +25217041536*n^3 +17311651344*n^4 +5993468992*n^5 +2592460808*n^6 +533444296*n^7 +163476113*n^8 +20735776*n^9 +4812092*n^10 +370160*n^11 +67942*n^12 +2912*n^13 +436*n^14 +8*n^15 +n^16) for n in (1..50)] # _G. C. Greubel_, Jan 24 2022
%Y A157058 Cf. A103881, A156554.
%K A157058 nonn,easy
%O A157058 1,1
%A A157058 _R. H. Hardin_, Feb 22 2009