A217436 Triangular array read by rows. T(n,k) is the number of labeled relations on n elements with exactly k vertices of indegree and outdegree = 0.

1, 1, 1, 13, 2, 1, 469, 39, 3, 1, 63577, 1876, 78, 4, 1, 33231721, 317885, 4690, 130, 5, 1, 68519123173, 199390326, 953655, 9380, 195, 6, 1, 562469619451069, 479633862211, 697866141, 2225195, 16415, 273, 7, 1, 18442242396353040817, 4499756955608552, 1918535448844, 1860976376, 4450390, 26264, 364, 8, 1

Offset

0,4

Comments

Row sums = 2^(n^2). First column (k = 0) is A173403.

Sum_{k=1,2,...,n} T(n,k)*k = A197927.

Links

Table of n, a(n) for n=0..44.

Formula

E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A173403.

Example

1,
1, 1,
13, 2, 1,
469, 39, 3, 1,
63577, 1876, 78, 4, 1,
33231721, 317885, 4690, 130, 5, 1,
68519123173, 199390326, 953655, 9380, 195, 6, 1

Mathematica

nn=6; s=Sum[Sum[(-1)^k Binomial[n, k] 2^(n-k)^2, {k, 0, n}] x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Exp[ y x] s, {x, 0, nn}], {x, y}] //Grid

Crossrefs

Sequence in context: A010223 A010222 A086266 * A040166 A100395 A051310

Adjacent sequences: A217433 A217434 A217435 * A217437 A217438 A217439

Keyword

nonn,tabl

Author

Geoffrey Critzer, Oct 02 2012

Status

approved