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A300756 Triangle T(n,k) read by rows: number of squarefree graphs on n nodes with k components. 5

%I #14 Apr 01 2022 22:06:17

%S 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,

%T 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,

%U 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

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

%C Multiset transform of A077269.

%H Max Alekseyev, <a href="/A300756/b300756.txt">Table of n, a(n) for n = 0..209</a>

%H <a href="/index/Sq#square_free">Index entries for sequences of squarefree graphs</a>

%F 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

%e The triangle starts in row n=0 with columnes 0<=k<=n as

%e 1

%e 0 1

%e 0 1 1

%e 0 2 1 1

%e 0 3 3 1 1

%e 0 8 5 3 1 1

%e 0 19 14 6 3 1 1

%e 0 57 33 16 6 3 1 1

%e 0 186 98 39 17 6 3 1 1

%e 0 740 305 116 41 17 6 3 1 1

%e 0 3389 1133 355 122 42 17 6 3 1 1

%e 0 18502 4824 1288 373 124 42 17 6 3 1 1

%e 0 120221 24575 5332 1343 379 125 42 17 6 3 1 1

%e 0 932260 150292 26415 5499 1361 381 125 42 17 6 3 1 1

%e 0 8596844 1110759 157791 26973 5554 1367 382 125 42 17 6 3 1 1

%e 0 93762704 9876826 1146376 159799 27146 5572 1369 382 125 42 17 6 3 1 1

%e 0 1201732437 104856709 10078812 1154493 160372 27201 5578 1370 382 125 42 17 6 3 1 1

%e 0 17992683043 1317129728 106250470 10116666 1156565 160545 27219 5580 1370 382 125 42 17 6 3 1 1

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

%K nonn,tabl

%O 0,8

%A _R. J. Mathar_, Mar 12 2018

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)