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A053729
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Self-convolution of 1,4,27,256,3125,46656,... (cf. A000312).
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3
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1, 8, 70, 728, 9027, 132136, 2254620, 44262200, 987183525, 24718587592, 687457908306, 21034757596184, 702270963692039, 25400848001674856, 989240042333246072, 41263578858484555512, 1835070614332428285513
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k^k * (n+1-k)^(n+1-k).
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EXAMPLE
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a(4) = 1^1 *4^4 +2^2 *3^3 +3^3 *2^2 +4^4 *1^1 = 1*256 +4*27 +27*4 +256*1 = 728.
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MATHEMATICA
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nn=20; f[x_]=Sum[n^n x^n, {n, 1, nn}]; CoefficientList[Series[f[x]^2/x^2, {x, 0, nn}], x] (* Geoffrey Critzer, Nov 05 2013 *)
Table[Sum[k^k*(n+1-k)^(n+1-k), {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 10 2018 *)
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PROG
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(Python)
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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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EXTENSIONS
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STATUS
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approved
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