A157054 Number of integer sequences of length n+1 with sum zero and sum of absolute values 10.
2, 30, 252, 1500, 7002, 27174, 91112, 271224, 731502, 1815506, 4197468, 9129276, 18827718, 37060506, 70006512, 127485584, 224676522, 384468534, 640622012, 1041949020, 1657762722, 2584888350, 3956576472, 5953712520, 8818775030, 12873059082, 18537751260
Offset: 1
Keywords
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
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Mathematica
Table[n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400, {n,50}] (* G. C. Greubel, Jan 23 2022 *) -
Sage
[n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400 for n in (1..50)] # G. C. Greubel, Jan 23 2022
Formula
a(n) = T(n,5); 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+4*x+16*x^2+24*x^3+36*x^4+24*x^5+16*x^6+4*x^7+x^8)/(1-x)^11. - Colin Barker, Mar 17 2012
From G. C. Greubel, Jan 23 2022: (Start)
a(n) = n*(n+1)*(n^8 +4*n^7 +66*n^6 +184*n^5 +1089*n^4 +1876*n^3 +4604*n^2 +3696*n +2880)/14400.
E.g.f.: (x/14400)*(28800 +187200*x +403200*x^2 +398400*x^3 +207840*x^4 +61200*x^5 +10400*x^6 +1000*x^7 +50*x^8 +x^9)*exp(x). (End)