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A103212
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a(n) = (1/n) * Sum_{i=0..n-1} C(n,i)*C(n,i+1)*(n-1)^i*n^(n-i) for n>=1, a(0)=1.
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2
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1, 1, 6, 93, 2380, 85405, 3956106, 224939113, 15175702200, 1185580310121, 105302043709390, 10482085765658661, 1156062800841590148, 139945327558704629221, 18449221488652046992914, 2631255715262150125502865, 403689862107153669227378416, 66297391981691913179574751633
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ 2^(2*n) * n^(n-3/2) / (sqrt(Pi) * exp(1/2)). - Vaclav Kotesovec, Sep 24 2017
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MATHEMATICA
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Table[HypergeometricPFQ[{-n, n+1}, {2}, -n+1], {n, 0, 20}] (* Vaclav Kotesovec, Sep 24 2017 *)
Flatten[{1, 1, Table[Sum[Binomial[n, k]*Binomial[n, k+1]*(n-1)^k*n^(n-k), {k, 0, n-1}]/n, {n, 2, 20}]}] (* Vaclav Kotesovec, Sep 24 2017 *)
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PROG
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(PARI) a(n) = {if(n==0, 1, sum(i=0, n-1, binomial(n, i)*binomial(n, i+1)*(n-1)^i*n^(n-i))/n)} \\ Andrew Howroyd, Apr 14 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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