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A063258
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Binomial(n+5,4)-1.
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10
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4, 14, 34, 69, 125, 209, 329, 494, 714, 1000, 1364, 1819, 2379, 3059, 3875, 4844, 5984, 7314, 8854, 10625, 12649, 14949, 17549, 20474, 23750, 27404, 31464, 35959, 40919, 46375, 52359, 58904, 66044, 73814, 82250, 91389, 101269, 111929, 123409, 135750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| In the Frey-Sellers reference this sequence is called {(n+2) over 4}_{3}, n >= 0.
If X is an n-set and Y a fixed (n-4)-subset of X then a(n-5) is equal to the number of 4-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Aug 15 2007
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REFERENCES
| D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
Milan Janjic, Two Enumerative Functions
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FORMULA
| a(n)= A062750(n+2, 4)= (n+6)*(n+1)*(n^2+7*n+16)/4!.
G.f.: N(4;1, x)/(1-x)^5 with N(4;1, x)= 4-6*x+4*x^2-x^3, polynomial of second row of A062751.
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MAPLE
| [seq(binomial(n, 4)-1, n=5..37)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
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MATHEMATICA
| s1=s2=s3=s4=0; lst={}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; If[(s3-2)/2>0, AppendTo[lst, (s3-2)/2]], {n, -1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 04 2009]
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PROG
| (PARI) { for (n=0, 1000, write("b063258.txt", n, " ", binomial(n + 5, 4) - 1) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 19 2009]
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CROSSREFS
| Fifth column (r=4) of FS(4) staircase array A062750.
A column of triangle A014473.
Cf. A000096, A062748.
Sequence in context: A098942 A011554 A099586 * A178964 A197275 A011852
Adjacent sequences: A063255 A063256 A063257 * A063259 A063260 A063261
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 12 2001
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EXTENSIONS
| Simpler definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 21 2003
More terms from Milan R. Janjic (agnus(AT)blic.net), Aug 15 2007
More terms from Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 19 2009
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