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%I #21 Sep 08 2022 08:44:59
%S 0,0,4,349,9985,213230,4000444,69940479,1170549895,19024433560,
%T 302846958634,4748624978009,73628721516805,1132119741733890,
%U 17298702716660824,263082403948681939,3986935934969727715
%N Number of 4-element intersecting families (of distinct sets) whose union is an n-element set.
%H G. C. Greubel, <a href="/A052391/b052391.txt">Table of n, a(n) for n = 1..845</a>
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (71, -2205, 39495, -452523, 3473673, -18166175, 64427005, -150923976, 220549356, -178819920, 59875200).
%F a(n) = (15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/4!.
%F G.f.: x^3*(14968800*x^8 - 25752870*x^7 + 16968966*x^6 - 5759365*x^5 + 1095624*x^4 - 115860*x^3 + 5974*x^2 - 65*x - 4)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(11*x-1)*(15*x-1)). - _Colin Barker_, Jul 30 2012
%t Table[(15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/4!, {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%t LinearRecurrence[{71,-2205,39495,-452523,3473673,-18166175,64427005,-150923976,220549356,-178819920,59875200},{0,0,4,349,9985,213230,4000444,69940479,1170549895,19024433560,302846958634},20] (* _Harvey P. Dale_, May 20 2018 *)
%o (PARI) for(n=0,50, print1((15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/24, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o (Magma) [(15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/24: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017
%Y Cf. A051181, A053152, A053153.
%K nonn,easy
%O 1,3
%A _Vladeta Jovovic_, Goran Kilibarda, Mar 11 2000
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