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Search: id:A062988
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| A062988 |
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a(n) = binomial(n+6,5)-1. |
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+0
7
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| 5, 20, 55, 125, 251, 461, 791, 1286, 2001, 3002, 4367, 6187, 8567, 11627, 15503, 20348, 26333, 33648, 42503, 53129, 65779, 80729, 98279, 118754, 142505, 169910, 201375, 237335, 278255, 324631
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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In the Frey-Sellers reference this sequence is called {(n+2) over 5}_{4}, n >= 0.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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a(n)= A062985(n+2, 5)= (n+1)*(n^4+19*n^3+136*n^2+444*n+600)/5!.
G.f.: N(5;1, x)/(1-x)^6 with N(5;1, x)= 5-10*x+10*x^2-5*x^3+x^4 = (1-(1-x)^5)/x, polynomial of second row of A062986.
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MAPLE
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[seq(binomial(n, 5)-1, n=6..35)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
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MATHEMATICA
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s1=s2=s3=s4=0; lst={}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s4/2-1], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 04 2009]
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PROGRAM
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(PARI) { for (n=0, 1000, write("b062988.txt", n, " ", binomial(n + 6, 5) - 1) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 15 2009]
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CROSSREFS
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Sixth column (r=5) of FS(5) staircase array A062985.
A column of triangle A014473.
Cf. A000096, A062748, A063258.
Sequence in context: A006010 A055383 A090133 this_sequence A038165 A032340 A011854
Adjacent sequences: A062985 A062986 A062987 this_sequence A062989 A062990 A062991
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 12 2001
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