A307806 Triangle T(n,k) read by rows: number of series-reduced labeled graphs on n nodes with k components.

1, 1, 1, 0, 3, 1, 5, 3, 6, 1, 51, 25, 15, 10, 1, 3634, 381, 90, 45, 15, 1, 374119, 26509, 1596, 280, 105, 21, 1, 73161880, 3095579, 111370, 5061, 770, 210, 28, 1, 26545249985, 671957334, 14411205, 353262, 13671, 1890, 378, 36, 1

Offset

1,5

Links

Table of n, a(n) for n=1..45.

Formula

T(n,1) = A003515(n).

T(n,k) = Sum_{Compositions n=n_1+n_2+...n_k, n_i>=1} multinomial(n; n_1,n_2,..,n_k) * T(n_1,1) * T(n_2,1) *... T(n_k,1)/ k!.

Example

The triangle starts
1;
1,1;
0,3,1;
5,3,6,1;
51,25,15,10,1;
3634,381,90,45,15,1;
374119,26509,1596,280,105,21,1;
73161880,3095579,111370,5061,770,210,28,1;
26545249985,671957334,14411205,353262,13671,1890,378,36,1;

Crossrefs

Cf. A003515 (column k=1), A003514 (row sums).

Sequence in context: A325685 A109606 A318727 * A127418 A099550 A349341

Adjacent sequences: A307803 A307804 A307805 * A307807 A307808 A307809

Keyword

nonn,tabl,easy

Author

R. J. Mathar, Apr 29 2019

Status

approved