A053729 Self-convolution of 1,4,27,256,3125,46656,... (cf. A000312).
1, 8, 70, 728, 9027, 132136, 2254620, 44262200, 987183525, 24718587592, 687457908306, 21034757596184, 702270963692039, 25400848001674856, 989240042333246072, 41263578858484555512, 1835070614332428285513
Offset: 1
Examples
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.
Links
- John Tyler Rascoe, Table of n, a(n) for n = 1..100
Programs
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Mathematica
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 *) -
Python
def A053729(n): return sum((k**k)*(n+1-k)**(n+1-k) for k in range(1,n+1)) # John Tyler Rascoe, Aug 23 2024
Formula
a(n) = Sum_{k=1..n} k^k * (n+1-k)^(n+1-k).
a(n) ~ 2 * n^n. - Vaclav Kotesovec, Mar 10 2018
Extensions
More terms from James Sellers, Feb 22 2000