A152291 a(n) = (n+1)^floor((n-1)/2).

1, 1, 1, 4, 5, 36, 49, 512, 729, 10000, 14641, 248832, 371293, 7529536, 11390625, 268435456, 410338673, 11019960576, 16983563041, 512000000000, 794280046581, 26559922791424, 41426511213649, 1521681143169024, 2384185791015625

Offset: 0

Author

Paul D. Hanna, Dec 02 2008

Keywords

• nonn

Crossrefs

Cf. A152290, A000272.

This is for Coxeter type A what A078707 is for Coxeter type B.

Programs

Magma

[(n+1)^((n-1) div 2): n in [0..30]]; // Vincenzo Librandi, May 31 2015

PARI

a(n)=(n+1)^floor((n-1)/2)

PARI

vector(30, n, n--; (n+1)^((n-1)\2)) \\ Michel Marcus, Jun 01 2015

Formula

Row sums of A152290 at q=-1: a(n) = Sum_{k=0..n(n-1)/2} A152290(n,k)*(-1)^k.

a(n) = denominator((-3+(-1)^n)*((1-sqrt(1+n+1/(1+n)))^n-(1+sqrt(1+n+1/(1+n)))^n)/(8*sqrt(1+n+1/(1+n)))). - Gerry Martens, May 31 2015