A305465 a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*n^(n-2*k).

1, 1, 9, 174, 6433, 387045, 34372513, 4223468872, 685727920641, 142133068151865, 36615156774045001, 11474421446955693006, 4298048476279871328289, 1896322606147540294800349, 973319784969445114237699713, 575000041101937659730069884960

Offset: 0

Author

Seiichi Manyama, Jun 02 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..232

Crossrefs

Main diagonal of A305401.

Cf. A021009, A305467.

Programs

Mathematica

Join[{1},Table[Sum[(n-k)!/k! Binomial[n-k,k]n^(n-2k),{k,0,Floor[n/2]}],{n,20}]] (* Harvey P. Dale, Sep 22 2019 *)

PARI

{a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*n^(n-2*k))}

Formula

a(n) ~ n! * n^n. - Vaclav Kotesovec, Jun 03 2018