The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A198261 Triangular array read by rows T(n,k) is the number of simple labeled graphs on n nodes with exactly k isolated nodes, 0<=k<=n. 0
 1, 0, 1, 1, 0, 1, 4, 3, 0, 1, 41, 16, 6, 0, 1, 768, 205, 40, 10, 0, 1, 27449, 4608, 615, 80, 15, 0, 1, 1887284, 192143, 16128, 1435, 140, 21, 0, 1, 252522481, 15098272, 768572, 43008, 2870, 224, 28, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums = 2^binomial(n,2) = A006125(n). First column (k=0) is A006129. LINKS FORMULA E.g.f. for column k: x^k/k! *A(x)/exp(x) where A(x) is the e.g.f. for A006125. T(n,n) = 1 (the empty graph). - Geoffrey Critzer, Nov 11 2011 T(n,n-1) = 0. - Geoffrey Critzer, Nov 11 2011 EXAMPLE 1; 0,       1; 1,       0,      1; 4,       3,      0,     1; 41,      16,     6,     0,    1; 768,     205,    40,    10,   0,   1; 27449,   4608,   615,   80,   15,  0,  1; 1887284, 192143, 16128, 1435, 140, 21, 0, 1; MATHEMATICA g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, 20}]; Transpose[Table[Range[0, 10]! CoefficientList[Series[(x^n/n!)( g/Exp[x]), {x, 0, 10}], x], {n, 0, 8}]]//Grid CROSSREFS Sequence in context: A327125 A152148 A270708 * A284056 A296002 A227423 Adjacent sequences:  A198258 A198259 A198260 * A198262 A198263 A198264 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Oct 22 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)