A092617 Number of connected ordered 5-element antichains on an unlabeled n-set.
0, 0, 0, 0, 30, 2065, 51926, 691686, 6185741, 42149926, 235537736, 1130582442, 4808698802, 18525169347, 65689136552, 217026359262, 674420929513, 1986166442853, 5577112808148, 15006708704808, 38855732384838, 97150869913209, 235268421882814, 553258656221514
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
- Index entries for linear recurrences with constant coefficients, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).
Programs
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PARI
concat(vector(4), Vec(x^4*(30 + 1135*x + 1861*x^2 - 92645*x^3 + 550840*x^4 - 1503530*x^5 + 1204830*x^6 + 6356840*x^7 - 30229830*x^8 + 73564425*x^9 - 122160215*x^10 + 145445855*x^11 - 117446220*x^12 + 41833425*x^13 + 45709685*x^14 - 103484155*x^15 + 113466775*x^16 - 87794190*x^17 + 51657460*x^18 - 23442310*x^19 + 8049625*x^20 - 1954899*x^21 + 262785*x^22 + 15815*x^23 - 16915*x^24 + 3970*x^25 - 470*x^26 + 24*x^27) / (1 - x)^31 + O(x^30))) \\ Colin Barker, Oct 13 2017
Formula
O.g.f.: 1/(-x+1)^31-20/(-x+1)^23+60/(-x+1)^19+20/(-x+1)^17+5/(-x+1)^16-105/(-x+1)^15-120/(-x+1)^14+150/(-x+1)^13+180/(-x+1)^12-300/(-x+1)^11-110/(-x+1)^10+380/(-x+1)^9+160/(-x+1)^8-575/(-x+1)^7+570/(-x+1)^6-186/(-x+1)^5-975/(-x+1)^4+1645/(-x+1)^3-1030/(-x+1)^2+274/(-x+1)-24 = 5!*A(-log(1-x)), where A(x) is e.g.f. for A094036.
G.f.: x^4*(30 + 1135*x + 1861*x^2 - 92645*x^3 + 550840*x^4 - 1503530*x^5 + 1204830*x^6 + 6356840*x^7 - 30229830*x^8 + 73564425*x^9 - 122160215*x^10 + 145445855*x^11 - 117446220*x^12 + 41833425*x^13 + 45709685*x^14 - 103484155*x^15 + 113466775*x^16 - 87794190*x^17 + 51657460*x^18 - 23442310*x^19 + 8049625*x^20 - 1954899*x^21 + 262785*x^22 + 15815*x^23 - 16915*x^24 + 3970*x^25 - 470*x^26 + 24*x^27) / (1 - x)^31. - Colin Barker, Oct 13 2017