A303728 Triangle read by rows: T(n,k) is the number of labeled cyclic subgroups of order k in the alternating group A_n, 1 <= k <= A051593(n).

1, 1, 1, 0, 1, 1, 3, 4, 1, 15, 10, 0, 6, 1, 45, 40, 45, 36, 1, 105, 175, 315, 126, 105, 120, 1, 315, 616, 1890, 336, 2520, 960, 0, 0, 0, 0, 0, 0, 0, 336, 1, 1323, 2884, 9450, 756, 18900, 4320, 0, 6720, 2268, 0, 3780, 0, 0, 3024, 1, 5355, 15520, 47250, 19656

Offset: 1

Author

Andrew Howroyd, Jul 03 2018

Keywords

• nonn
• tabf

Examples

			Triangle begins:
1;
1;
1, 0, 1;
1, 3, 4;
1, 15, 10, 0, 6;
1, 45, 40, 45, 36;
1, 105, 175, 315, 126, 105, 120;
1, 315, 616, 1890, 336, 2520, 960, 0, 0, 0, 0, 0, 0, 0, 336;
...
		

Crossrefs

Row sums are A051636.

Cf. A051593, A074881, A181950.

Programs

PARI

permcount(v) = {my(m=1,s=0,k=0,t); for(i=1,#v,t=v[i]; k=if(i>1&&t==v[i-1],k+1,1); m*=t*k;s+=t); s!/m}
G(n)={my(s=0); forpart(p=n, if(sum(i=1,#p,p[i]-1)%2==0, my(d=lcm(Vec(p))); s+=x^d*permcount(p)/eulerphi(d))); s}
for(n=1, 10, print(Vecrev(G(n)/x)))