3,1

For analogue with regular (not centered) n-gonal numbers, see A133401. Array A[k,n] = k-th Polygorial(n,k) begins:

k..|..CenteredPolygorial(n,k)

3..|.1.4...40...760...23560....1083760......69360640......5895654400...A140701

4..|.1.5...65..1625...66625....4064125.....345450625.....39035920625...

5..|.1.6...96..2976...151776...11534976...1222707456....172401751296...

6..|.1.7..133..4921...300181...27316471...3469191817....586293417073...

7..|.1.8..176..7568...537328...56956768...8429601664...1660631527808...

8..|.1.9..225.11025...893025..108056025..18261468225...4108830350625...

9..|.1.10.280.15400..1401400..190590400..36212176000...9161680528000...

Eric W. Weisstein, Centered Triangular Number.

a(3) = 3rd Centered Polygorial number Polygorial(3,3) = A140701(3) = product of the first 3 centered triangular numbers = 1 * 4 * 10 = 40.

a(4) = 4th Centered Polygorial number Centered Polygorial(4,4) = product of the first 4 centered square numbers A001844 = 1 * 5 * 13 * 25 = 1625.

a(5) = 5th Centered Pentagorial number Centered Polygorial(5,5) = product of the first 5 centered pentagonal numbers A005891 = 1 * 5 * 12 * 22 * 35 = 151776.

a(6) = 6th Centered Hexagorial number Centered Polygorial(6,6) = product of the first 6 centered hexagonal numbers A003215 = 1 * 7 * 19 * 37 * 61 * 91 = 27316471.

Cf. A005448, A006003, A006472, A133401, A140701.

Sequence in context: A158703 A009984 A041761 this_sequence A145294 A147520 A143314

Adjacent sequences: A140699 A140700 A140701 this_sequence A140703 A140704 A140705

easy,more,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), May 24 2008