A349893 a(n) = Sum_{k=0..n} k^(k*(n-k)).

1, 2, 3, 7, 46, 1052, 88603, 27121965, 37004504306, 198705527223758, 5595513387083114571, 686714367475480207331583, 468422339816915120237104999422, 1664212116512828935888786624225704856, 31295654819650678010096952493864470025103251

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..52

Formula

G.f.: Sum_{k>=0} x^k/(1 - k^k * x).

log(a(n)) ~ n^2*log(n)/4 * (1 - log(2)/log(n) + 1/(4*log(n)^2)). - Vaclav Kotesovec, Dec 05 2021

Mathematica

Table[1 + Sum[k^(k*(n - k)), {k, 1, n}], {n, 0, 16}] (* Vaclav Kotesovec, Dec 05 2021 *)

Prog

(PARI) a(n) = sum(k=0, n, k^(k*(n-k)));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^k*x)))

Crossrefs

Cf. A117402, A349880, A349881, A349886, A349894.

Sequence in context: A032053 A343522 A086542 * A058181 A198959 A000231

Adjacent sequences: A349890 A349891 A349892 * A349894 A349895 A349896

Keyword

nonn

Author

Seiichi Manyama, Dec 04 2021

Status

approved