A157055 Number of integer sequences of length n+1 with sum zero and sum of absolute values 12.
2, 36, 362, 2570, 14240, 65226, 256508, 889716, 2777370, 7925720, 20934474, 51697802, 120353324, 265953170, 561075720, 1135620536, 2214405618, 4175000796, 7634582090, 13577591370, 23539760552, 39868752506, 66087441092, 107392877100, 171332460650, 268708978512
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
Programs
-
Mathematica
Table[n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400, {n, 50}] (* G. C. Greubel, Jan 24 2022 *) -
Sage
[n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400 for n in (1..50)] # G. C. Greubel, Jan 24 2022
Formula
a(n) = T(n,6) where T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
G.f.: 2*x*(1 +5*x +25*x^2 +50*x^3 +100*x^4 +100*x^5 +100*x^6 +50*x^7 +25*x^8 +5*x^9 +x^10)/(1-x)^13. - Colin Barker, Jan 25 2013
From G. C. Greubel, Jan 24 2022: (Start)
a(n) = n*(n+1)*(n^10 +5*n^9 +120*n^8 +450*n^7 +4173*n^6 +10965*n^5 +48530*n^4 +79300*n^3 +163176*n^2 +125280*n +86400)/518400.
E.g.f.: (x/518400)*(1036800 +8294400*x +22464000*x^2 +28728000*x^3 +20131200*x^4 +8369280*x^5 +2154240*x^6 +349200*x^7 +35400*x^8 +2160*x^9 +72*x^10 +x^11)*exp(x). (End)