This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056090 #27 Feb 16 2025 08:32:43
%S A056090 25,429,3364,17602,71385,242347,720792,1934076,4777337,11021713,
%T A056090 24008532,49790614,98954626,189457350,350941064,631167840,1105440045,
%U A056090 1890167329,3162113836,5185330818,8348369731,13215102985,20593381200,31626858540,47916657405,71681161365
%N A056090 Number of 4-element ordered antichain covers of an unlabeled n-element set.
%D A056090 V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
%D A056090 V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H A056090 G. C. Greubel, <a href="/A056090/b056090.txt">Table of n, a(n) for n = 4..1000</a>
%H A056090 K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%H A056090 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cover.html">Antichain covers</a>
%H A056090 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).
%F A056090 a(n) = C(n + 14, 14) - 12*C(n + 10, 10) + 24*C(n + 8, 8) + 4*C(n + 7, 7) - 18*C(n + 6, 6) + 6*C(n + 5, 5) - 36*C(n + 4, 4) + 36*C(n + 3, 3) + 11*C(n + 2, 2) - 22*C(n + 1, 1) + 6*C(n, 0).
%F A056090 G.f.: x^4*(6*x^10 -62*x^9 +271*x^8 -636*x^7 +800*x^6 -328*x^5 -495*x^4 +812*x^3 -446*x^2 +54*x +25)/(1-x)^15. - _Colin Barker_, May 29 2012
%F A056090 a(n) = (-104270181120 n + 236073062016 n^2 - 169534943760 n^3 + 28403538800 n^4 + 12862329480 n^5 - 2983956976 n^6 - 613678065 n^7 + 39763295 n^8 + 21456435 n^9 + 2461459 n^10 + 143325 n^11 + 5005 n^12 + 105 n^13 + n^14)/(14)!. - _G. C. Greubel_, Oct 06 2017
%t A056090 Table[(-104270181120 n + 236073062016 n^2 - 169534943760 n^3 + 28403538800 n^4 + 12862329480 n^5 - 2983956976 n^6 - 613678065 n^7 + 39763295 n^8 + 21456435 n^9 + 2461459 n^10 + 143325 n^11 + 5005 n^12 + 105 n^13 + n^14)/(14)!, {n, 4, 50}] (* _G. C. Greubel_, Oct 06 2017 *)
%t A056090 LinearRecurrence[{15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1},{25,429,3364,17602,71385,242347,720792,1934076,4777337,11021713,24008532,49790614,98954626,189457350,350941064},30] (* _Harvey P. Dale_, Dec 09 2021 *)
%o A056090 (PARI) for(n=4,50, print1((-104270181120*n + 236073062016*n^2 - 169534943760*n^3 + 28403538800*n^4 + 12862329480*n^5 - 2983956976*n^6 - 613678065*n^7 + 39763295*n^8 + 21456435*n^9 + 2461459*n^10 + 143325*n^11 + 5005*n^12 + 105*n^13 + n^14)/(14)!, ", ")) \\ _G. C. Greubel_, Oct 06 2017
%o A056090 (Magma) [(-104270181120*n + 236073062016*n^2 - 169534943760*n^3 + 28403538800*n^4 + 12862329480*n^5 - 2983956976*n^6 - 613678065*n^7 + 39763295*n^8 + 21456435*n^9 + 2461459*n^10 + 143325*n^11 + 5005*n^12 + 105*n^13 + n^14)/Factorial(14): n in [4..50]]; // _G. C. Greubel_, Oct 06 2017
%Y A056090 Cf. A056047 for 4-antichain (unordered) covers of a labeled n-set, A051112. See also A056074, A056093.
%K A056090 nonn
%O A056090 4,1
%A A056090 _Vladeta Jovovic_, Goran Kilibarda, Jul 27 2000