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A157053
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Number of integer sequences of length n+1 with sum zero and sum of absolute values 8.
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1
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2, 24, 162, 780, 2970, 9492, 26474, 66222, 151560, 322190, 643632, 1219374, 2206932, 3838590, 6447660, 10501172, 16639974, 25727292, 38906870, 57671880, 83945862, 120177024, 169447302, 235597650, 323371100, 438575202, 588265524, 780951962, 1026829680
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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,4); 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+3*x+9*x^2+9*x^3+9*x^4+3*x^5+x^6)/(1-x)^9. - Colin Barker, Mar 17 2012
a(n) = n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576. - Bruno Berselli, Mar 17 2012
E.g.f.: (x/576)*(1152 +5760*x +9216*x^2 +6432*x^3 +2208*x^4 +384*x^5 +32*x^6 +x^7)*exp(x). - G. C. Greubel, Jan 23 2022
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MATHEMATICA
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Table[n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576, {n, 50}] (* G. C. Greubel, Jan 23 2022 *)
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PROG
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(Sage) [n*(n+1)*(n^2+n+6)*(n^4 +2*n^3 +23*n^2 +22*n +24)/576 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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