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 A060052 Triangle read by rows: T(n,k) gives number of r-bicoverings of an n-set with k blocks, n >= 2, k = 3..n+floor(n/2). 11
 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 (list; graph; refs; listen; history; text; internal format)
 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 Row sums are A060053. Column sums are A060051. Cf. A059443, A059530, A060092, A060487, A060492, A276640, A331039. Sequence in context: A141150 A081162 A095367 * A059065 A170771 A170772 Adjacent sequences:  A060049 A060050 A060051 * A060053 A060054 A060055 KEYWORD easy,nonn,tabf AUTHOR Vladeta Jovovic, Feb 15 2001 EXTENSIONS Zeros inserted into data by Andrew Howroyd, Jan 30 2020 STATUS approved

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Last modified June 24 20:41 EDT 2021. Contains 345425 sequences. (Running on oeis4.)