A155956 a(n) = Sum_{k=0..n} (k*n)^k.

1, 2, 19, 769, 67333, 9929106, 2201420095, 683765250589, 283214405613321, 150820803395086078, 100389106493001087411, 81663040762574177095289, 79709457342800206602843277, 91941570967455757927336110570, 123717598784707453088183544702311

Offset: 0

Author

Reinhard Zumkeller, Jan 31 2009

Keywords

• nonn

Comments

Sums of rows of the triangle in A155955.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..210

Crossrefs

Cf. A000312.

Programs

Magma

[&+[(k*n)^k: k in [0..n]]: n in [0..20]]; // Bruno Berselli, Jul 04 2016

Mathematica

Table[Sum[(k*n)^k,{k,n}],{n,0,20}]+1 (* Harvey P. Dale, Apr 04 2017 *)

PARI

vector(30, n, n--; sum(k=0,n, (k*n)^k)) \\ G. C. Greubel, Sep 14 2018

Formula

a(n) = h(n,n) with h(n,k) = if k<0 then 0 otherwise n*h(n,k-1)+(n-k)^(n-k).