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A157052
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Number of integer sequences of length n+1 with sum zero and sum of absolute values 6.
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2
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2, 18, 92, 340, 1010, 2562, 5768, 11832, 22530, 40370, 68772, 112268, 176722, 269570, 400080, 579632, 822018, 1143762, 1564460, 2107140, 2798642, 3670018, 4756952, 6100200, 7746050, 9746802, 12161268, 15055292, 18502290, 22583810, 27390112, 33020768, 39585282
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = T(n,3); 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+2*x+4*x^2+2*x^3+x^4)/(1-x)^7. - Colin Barker, Mar 17 2012
a(n) = n*(n+1)*(n^4 +2*n^3 +11*n^2 +10*n +12)/36. - Bruno Berselli, Mar 17 2012
E.g.f.: (x/36)*(72 + 252*x + 264*x^2 + 108*x^3 + 18*x^4 + x^5)*exp(x). - G. C. Greubel, Jan 23 2022
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MAPLE
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MATHEMATICA
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Table[n(n+1)(n^4 +2n^3 +11n^2 +10n +12)/36, {n, 50}] (* Wesley Ivan Hurt, Feb 03 2014 *)
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PROG
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(Sage) [n*(n+1)*(n^4 +2*n^3 +11*n^2 +10*n +12)/36 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,easy
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AUTHOR
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STATUS
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approved
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