OFFSET
2,3
COMMENTS
A bicovering is r-bicovering if intersection of every two blocks contains at most one element.
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1802 (rows n=2..50)
FORMULA
E.g.f.: A(x, y) = exp(-x-1/2*x^2*y)*Sum_{i>=0} (1+y)^binomial(i, 2)*x^i/i!.
T(n, k) = (n!/k!) * A276640(k, n). - David Pasino, Sep 22 2016
T(n,k) = 0 for n > binomial(k,2). - Andrew Howroyd, Jan 30 2020
EXAMPLE
Triangle starts:
[1],
[1, 4],
[0, 15, 25, 3],
[0, 30, 222, 226, 40],
[0, 30, 1230, 3670, 2706, 535, 15],
[0, 0, 5040, 39900, 69450, 40405, 8141, 420],
[0, 0, 15120, 345240, 1254960, 1498035, 722275, 142877, 9730, 105],
[0, 0, 30240, 2492280, 18587520, 40701780, 36450820, 15031204, 2871240, 226828, 5040],
...
PROG
(PARI) \\ returns k-th column as vector.
C(k)=if(k<3, [], Vecrev(serlaplace(polcoef(exp(-x-1/2*x^2*y + O(x*x^k))*sum(i=0, 3*k\2, (1+y)^binomial(i, 2)*x^i/i!), k))/y)) \\ Andrew Howroyd, Jan 30 2020
(PARI)
T(n)={my(m=(3*n\2), y='y + O('y^(n+1))); my(g=exp(-x-1/2*x^2*y + O(x*x^m))*sum(k=0, m, (1+y)^binomial(k, 2)*x^k/k!)); Mat([Col(serlaplace(p), -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
KEYWORD
easy,nonn,tabf
AUTHOR
Vladeta Jovovic, Feb 15 2001
EXTENSIONS
Zeros inserted into data by Andrew Howroyd, Jan 30 2020
STATUS
approved