A300756 Triangle T(n,k) read by rows: number of squarefree graphs on n nodes with k components.

1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 3, 3, 1, 1, 0, 8, 5, 3, 1, 1, 0, 19, 14, 6, 3, 1, 1, 0, 57, 33, 16, 6, 3, 1, 1, 0, 186, 98, 39, 17, 6, 3, 1, 1, 0, 740, 305, 116, 41, 17, 6, 3, 1, 1, 0, 3389, 1133, 355, 122, 42, 17, 6, 3, 1, 1, 0, 18502, 4824, 1288, 373, 124, 42, 17, 6, 3, 1, 1, 0, 120221, 24575, 5332, 1343

Offset: 0

Author

R. J. Mathar, Mar 12 2018

Keywords

• nonn
• tabl

Comments

Multiset transform of A077269.

Examples

			The triangle starts in row n=0 with columnes 0<=k<=n as
1
0 1
0 1 1
0 2 1 1
0 3 3 1 1
0 8 5 3 1 1
0 19 14 6 3 1 1
0 57 33 16 6 3 1 1
0 186 98 39 17 6 3 1 1
0 740 305 116 41 17 6 3 1 1
0 3389 1133 355 122 42 17 6 3 1 1
0 18502 4824 1288 373 124 42 17 6 3 1 1
0 120221 24575 5332 1343 379 125 42 17 6 3 1 1
0 932260 150292 26415 5499 1361 381 125 42 17 6 3 1 1
0 8596844 1110759 157791 26973 5554 1367 382 125 42 17 6 3 1 1
0 93762704 9876826 1146376 159799 27146 5572 1369 382 125 42 17 6 3 1 1
0 1201732437 104856709 10078812 1154493 160372 27201 5578 1370 382 125 42 17 6 3 1 1
0 17992683043 1317129728 106250470 10116666 1156565 160545 27219 5580 1370 382 125 42 17 6 3 1 1
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..209
• Index entries for sequences of squarefree graphs

Crossrefs

Cf. A077269 (column k=1), A006786 (row sums).

Formula

G. f.: Sum_{n >= k >= 0} T(n,k)*x^n*y^k = exp( Sum_{m>=1} F(x^m)*y^m/m ), where F(y) is the generating function for A077269. - Max Alekseyev, Mar 30 2022