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A157054
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Number of integer sequences of length n+1 with sum zero and sum of absolute values 10.
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1
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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
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OFFSET
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1,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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FORMULA
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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
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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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