

A217563


Irregular triangular array read by rows. T(n,k) is the number of weakly connected relations on n labeled nodes with k arcs. (n>=0, 0<=k<=n^2)


0



1, 1, 1, 0, 2, 5, 4, 1, 0, 0, 12, 56, 111, 123, 84, 36, 9, 1, 0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 2000, 21104, 109400, 373920, 950725, 1915405, 3168880, 4394760, 5169230, 5188390, 4454000
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OFFSET

0,5


COMMENTS

Row sums = A062738.


LINKS

Table of n, a(n) for n=0..49.


FORMULA

E.g.f.: Log[Sum_{n>=0} (1+y)^(n^2) x^n/n!] + 1


EXAMPLE

1,
1, 1,
0, 2, 5, 4, 1,
0, 0, 12, 56, 111, 123, 84, 36, 9, 1,
0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1


MATHEMATICA

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


CROSSREFS

Cf. A062735.
Sequence in context: A324057 A106315 A285295 * A254881 A100946 A200019
Adjacent sequences: A217560 A217561 A217562 * A217564 A217565 A217566


KEYWORD

nonn,tabf


AUTHOR

Geoffrey Critzer, Oct 07 2012


STATUS

approved



