A252709 Sum_{k=0..n} k^(n+k)*(n-k)^k.

0, 1, 34, 2446, 315788, 66140883, 21216724582, 10063816019004, 6854671838281696, 6482951652242448021, 8197210060548767881834, 13365577359964731097098090, 27292891758122129732383863668, 68341049055686519197950975142247, 206830351842829303737616801603098478

Offset: 1

Author

Vaclav Kotesovec, Dec 20 2014

Keywords

• nonn
• easy

Crossrefs

Cf. A062817, A252708, A252710.

Programs

Mathematica

Table[Sum[k^(n+k)*(n-k)^k, {k, 0, n}], {n, 1, 15}]

Formula

log(a(n)) ~ n*(3*log(n)- log(log(n)) - 1 - log(2) + (log(log(n)) + log(2) - 2) / (2*log(n))). - Vaclav Kotesovec, Nov 22 2021