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A052389
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Number of 4-element intersecting families (with not necessarily distinct sets) of an n-element set.
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1
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0, 1, 9, 95, 1286, 20681, 360964, 6452825, 114920766, 2018035121, 34864971944, 593281456505, 9965368457746, 165615181710161, 2728984827320124, 44665923097267385, 727216852411490726, 11791672548220250801
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (83, -3052, 65670, -919413, 8804499, -58966886, 277278100, -904270136, 1982352768, -2749917312, 2142305280, -696729600).
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FORMULA
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a(n) = (16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24.
G.f.: x * (118224000*x^10 - 215558352*x^9 + 171543508*x^8 - 77761264*x^7 + 22230235*x^6 - 4199119*x^5 + 532266*x^4 - 44801*x^3 + 2400*x^2 - 74*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) * (10*x-1) * (12*x-1) * (16*x-1) ). - Colin Barker, Jul 30 2012
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MATHEMATICA
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Table[(16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
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PROG
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(PARI) for(n=0, 50, print1((16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24, ", ")) \\ G. C. Greubel, Oct 08 2017
(Magma) [(16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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