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Search: id:A062966
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| A062966 |
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C(3+n,n)+C(4+n,n)+C(5+n,n)+C(6+n,n). |
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+0
2
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| 4, 22, 74, 195, 441, 896, 1680, 2958, 4950, 7942, 12298, 18473, 27027, 38640, 54128, 74460, 100776, 134406, 176890, 229999, 295757, 376464, 474720, 593450, 735930, 905814, 1107162, 1344469, 1622695, 1947296
(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 6}_{3}, n >= 0.
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REFERENCES
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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
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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)= A062750(n+2, 6)= (n+10)*(n+3)*(n+2)*(n+1)*(n^2+11*n+48)/6!.
G.f.: N(4;1, x)/(1-x)^7 with N(4;1, x)= 4-6*x+4*x^2-x^3, polynomial of second row of A062751.
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PROGRAM
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(PARI) { for (n=0, 1000, a=binomial(3 + n, n) + binomial(4 + n, n) + binomial(5 + n, n) + binomial(6 + n, n); write("b062966.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 14 2009]
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CROSSREFS
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Seventh column (r=6) of FS(4) staircase array A062750.
Partial sums of A027659.
Sequence in context: A106846 A086863 A052149 this_sequence A078155 A096167 A060453
Adjacent sequences: A062963 A062964 A062965 this_sequence A062967 A062968 A062969
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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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EXTENSIONS
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Better description from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 02 2005
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