A094737 Number of connected 5-element multiantichains on a labeled n-set.
0, 1, 1, 19, 387, 12796, 588332, 30409555, 1510137553, 68451901642, 2839832714238, 109655179461961, 4007814663515939, 140559147215148208, 4779718456846032064, 158823449312897655487, 5186933187595033751445
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..670
Programs
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Mathematica
Table[ (3434 - 1095*4^n + 5*16^n - 3545*2^(n + 1) + 5*2^(3 n + 5) + 6665*3^n + 860*9^n + 5*4^(n + 1)*3^(n + 2) - 2106*5^n - 17*3^n*5^(n + 1) + 185*6^(n + 1) - 15*2^(n + 3)*7^n - 15*7^(n + 2) - 11*10^(n + 1) - 540*11^n + 150*13^n + 20*17^n + 60*19^n - 20*23^n + 31^n)/120 (1 - UnitStep[-n]), {n, 0, 20}] (* Benedict W. J. Irwin, May 25 2016 *)
Formula
E.g.f.: (1/5!)*(exp(31*x) -20*exp(23*x) +60*exp(19*x) +20*exp(17*x) +5*exp(16*x) -85*exp(15*x) -120*exp(14*x) +150*exp(13*x) +180*exp(12*x) -540*exp(11*x) -110*exp(10*x) +860*exp(9*x) +160*exp(8*x) -735*exp(7*x) +1110*exp(6*x) -2106*exp(5*x) -1095*exp(4*x) +6665*exp(3*x) -7090*exp(2*x) +3434*exp(x)-744).
a(n) = (3434 - 1095*4^n + 5*16^n - 3545*2^(n+1) + 5*2^(3n+5) + 6665*3^n + 860*9^n + 5*4^(n+1)*3^(n+2) - 2106*5^n - 17*3^n*5^(n+1) + 185*6^(n+1) - 15*2^(n+3)*7^n - 15*7^(n+2) - 11*10^(n+1) - 540*11^n + 150*13^n + 20*17^n + 60*19^n - 20*23^n + 31^n)/120, n>0. - Benedict W. J. Irwin, May 25 2016