A060095 Number of 7-block ordered bicoverings of an unlabeled n-set.

0, 0, 0, 0, 0, 1680, 27342, 208302, 1099602, 4636072, 16734438, 53810484, 158053119, 431305959, 1106791524, 2694914978, 6269281305, 14010246285, 30208869495, 63074014815, 127909521180, 252581107180, 486738385140

Offset

0,6

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Formula

a(n) = binomial(n+20, n) - 7*binomial(n+14, 14) - 21*binomial(n+10, 10) + 42*binomial(n+9, 9) + 105*binomial(n+6, 6) - 140*binomial(n+5, 5) + 105*binomial(n+4, 4) - 420*binomial(n+3, 3) + 35*binomial(n+2, 2) + 1050*binomial(n+1, 1) - 1050*binomial(n, 0) + 300*binomial(n-1, -1).

G.f.: y^5*(-1680 - 7005635*y^7 + 5039622*y^6 - 2707236*y^5 + 1022210*y^4 - 232680*y^3 + 13080*y^2 + 7938*y - 5250*y^15 + 300*y^16 + 43050*y^14 - 6227505*y^9 + 4042780*y^10 + 7485450*y^8 - 219485*y^13 + 778260*y^12 - 2033220*y^11)/(-1 + y)^21.

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} 1/(1 - y)^binomial(k, 2)*x^k/k!.

Prog

(PARI) a(n) = if(n<1, 0, binomial(n + 20, n) - 7*binomial(n + 14, 14) - 21*binomial(n + 10, 10) + 42*binomial(n + 9, 9) + 105*binomial(n + 6, 6) - 140*binomial(n + 5, 5) + 105*binomial(n + 4, 4) - 420*binomial(n + 3, 3) + 35*binomial(n + 2, 2) + 1050*binomial(n + 1, 1) - 1050*binomial(n, 0) + 300*binomial(n - 1, - 1)) \\ Harry J. Smith, Jul 01 2009

Crossrefs

Column k=7 of A060092.

Cf. A059948, A060090.

Sequence in context: A175340 A181928 A234439 * A343459 A282402 A156422

Adjacent sequences: A060092 A060093 A060094 * A060096 A060097 A060098

Keyword

nonn

Author

Vladeta Jovovic, Feb 26 2001

Status

approved