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

Table of n, a(n) for n=1..17.

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 *)

Crossrefs

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