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A053729
Self-convolution of 1,4,27,256,3125,46656,... (cf. A000312).
3
1, 8, 70, 728, 9027, 132136, 2254620, 44262200, 987183525, 24718587592, 687457908306, 21034757596184, 702270963692039, 25400848001674856, 989240042333246072, 41263578858484555512, 1835070614332428285513
OFFSET
1,2
LINKS
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
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
Sequence in context: A123511 A322416 A287482 * A266433 A267244 A228388
KEYWORD
nonn,easy
AUTHOR
Leroy Quet, Feb 11 2000
EXTENSIONS
More terms from James A. Sellers, Feb 22 2000
STATUS
approved