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

1,2

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..100

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

Cf. A000312, A100262.

Sequence in context: A123511 A322416 A287482 * A266433 A267244 A228388

Adjacent sequences: A053726 A053727 A053728 * A053730 A053731 A053732

Keyword

nonn,easy

Author

Leroy Quet, Feb 11 2000

Extensions

More terms from James A. Sellers, Feb 22 2000

Status

approved