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A052390 Number of 4-element intersecting families (with not necessarily distinct sets) whose union is an n-element set.

%I A052390 #23 Jan 29 2023 19:18:46
%S A052390 1,7,71,956,15116,254397,4318511,72331966,1188180386,19152566087,
%T A052390 303768582701,4755204310776,73675434833456,1132450098258577,
%U A052390 17301032324486891,263098797953058386,3987051131522775326
%N A052390 Number of 4-element intersecting families (with not necessarily distinct sets) whose union is an n-element set.
%H A052390 G. C. Greubel, <a href="/A052390/b052390.txt">Table of n, a(n) for n = 1..845</a>
%H A052390 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 A052390 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 A052390 <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 A052390 a(n) = (15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/4!.
%F A052390 G.f.: -x * (14968800*x^10 - 34931250*x^9 + 36757686*x^8 - 21625925*x^7 + 7809481*x^6 - 1821016*x^5 + 279853*x^4 - 28145*x^3 + 1779*x^2 - 64*x + 1) / ((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 A052390 Table[(15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/4!, {n, 1, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%o A052390 (PARI) for(n=1,50, print1((15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/4!, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o A052390 (Magma) [(15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/24: n in [1..50]]; // _G. C. Greubel_, Oct 08 2017
%Y A052390 Cf. A051181, A053156, A053157.
%K A052390 nonn,easy
%O A052390 1,2
%A A052390 _Vladeta Jovovic_, Goran Kilibarda, Mar 11 2000