cp's OEIS Frontend

A157056 Number of integer sequences of length n+1 with sum zero and sum of absolute values 14.

%I A157056 #17 Jan 24 2022 16:08:22
%S A157056 2,42,492,4060,26070,137886,623576,2476296,8809110,28512110,85014204,
%T A157056 235895244,614266354,1511679210,3536846160,7907476016,16967926746,
%U A157056 35078339106,70098276620,135798494460,255689552382,468969729382,839584669992,1469778991800,2520031983950
%N A157056 Number of integer sequences of length n+1 with sum zero and sum of absolute values 14.
%H A157056 T. D. Noe, <a href="/A157056/b157056.txt">Table of n, a(n) for n = 1..1000</a>
%H A157056 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F A157056 a(n) = T(n,7); T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
%F A157056 G.f.: 2*x*(1 +6*x +36*x^2 +90*x^3 +225*x^4 +300*x^5 +400*x^6 +300*x^7 +225*x^8 +90*x^9 +36*x^10 +6*x^11 +x^12)/(1-x)^15. - _Colin Barker_, Jan 25 2013
%F A157056 From _G. C. Greubel_, Jan 24 2022: (Start)
%F A157056 a(n) = n*(n+1)*(n^12 +6*n^11 +197*n^10 +930*n^9 +12363*n^8 +43938*n^7 +300551*n^6 +751710*n^5 +2756536*n^4 +4309656*n^3 +7816752*n^2 +5780160*n +3628800)/25401600.
%F A157056 E.g.f.: (x/25401600)*(50803200 +482630400*x +1574899200*x^2 +2472422400*x^3 +2176070400*x^4 +1169320320*x^5 +403683840*x^6 +92221920*x^7 +14129640*x^8 +1449420*x^9 +97608*x^10 +4116*x^11 +98*x^12 +x^13)*exp(x). (End)
%t A157056 Table[n*(n+1)*(n^12 +6*n^11 +197*n^10 +930*n^9 +12363*n^8 +43938*n^7 +300551*n^6 +751710*n^5 +2756536*n^4 +4309656*n^3 +7816752*n^2 +5780160*n +3628800)/25401600, {n,50}] (* _G. C. Greubel_, Jan 24 2022 *)
%o A157056 (Sage) [n*(n+1)*(n^12 +6*n^11 +197*n^10 +930*n^9 +12363*n^8 +43938*n^7 +300551*n^6 +751710*n^5 +2756536*n^4 +4309656*n^3 +7816752*n^2 +5780160*n +3628800)/25401600 for n in (1..50)] # _G. C. Greubel_, Jan 24 2022
%Y A157056 Cf. A103881, A156554.
%K A157056 nonn,easy
%O A157056 1,1
%A A157056 _R. H. Hardin_, Feb 22 2009