A060092 Triangle T(n,k) of k-block ordered bicoverings of an unlabeled n-set, n >= 2, k = 3..n+floor(n/2).

3, 7, 16, 12, 63, 125, 90, 18, 162, 722, 1716, 1680, 25, 341, 2565, 11350, 27342, 29960, 7560, 33, 636, 7180, 49860, 208302, 503000, 631512, 302400, 42, 1092, 17335, 173745, 1099602, 4389875, 10762299, 14975730, 9632700, 1247400

Offset

2,1

Comments

All columns are polynomials of order binomial(k, 2). - Andrew Howroyd, Jan 30 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 2..1802

Formula

E.g.f. for k-block ordered bicoverings of an unlabeled n-set is exp(-x-x^2/2*y/(1-y))*Sum_{k=0..inf} 1/(1-y)^binomial(k, 2)*x^k/k!.

Example

[3],
[7, 16],
[12, 63, 125, 90],
[18, 162, 722, 1716, 1680],
[25, 341, 2565, 11350, 27342, 29960, 7560],
[33, 636, 7180, 49860, 208302, 503000, 631512, 302400],
[42, 1092, 17335, 173745, 1099602, 4389875, 10762299, 14975730, 9632700, 1247400], ...
There are 23=7+16 ordered bicoverings of an unlabeled 3-set: 7 3-block bicoverings and 16 4-block bicoverings, cf. A060090.

Prog

(PARI) \\ gives g.f. of k-th column.
ColGf(k) = k!*polcoef(exp(-x - x^2*y/(2*(1-y)) + O(x*x^k))*sum(j=0, k, 1/(1-y)^binomial(j, 2)*x^j/j!), k) \\ Andrew Howroyd, Jan 30 2020
(PARI)
T(n)={my(m=(3*n\2), y='y + O('y^(n+1))); my(g=serlaplace(exp(-x - x^2*y/(2*(1-y)) + O(x*x^m))*sum(k=0, m, 1/(1-y)^binomial(k, 2)*x^k/k!))); Mat([Col(p/y^2, -n) | p<-Vec(g)[2..m+1]])}
{ my(A=T(8)); for(n=2, matsize(A)[1], print(A[n, 3..3*n\2])) } \\ Andrew Howroyd, Jan 30 2020

Crossrefs

Row sums are A060090.

Columns k=3..7 are A055998(n-1), A060091, A060093, A060094, A060095.

Cf. A059443, A060052, A060487, A060492, A094573, A331571.

Sequence in context: A153578 A018852 A260465 * A035283 A184863 A162159

Adjacent sequences: A060089 A060090 A060091 * A060093 A060094 A060095

Keyword

nonn,tabf

Author

Vladeta Jovovic, Feb 26 2001

Status

approved