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A210569
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(n-3)(n-2)(n-1)n(n+1)/30.
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5
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0, 0, 0, 0, 4, 24, 84, 224, 504, 1008, 1848, 3168, 5148, 8008, 12012, 17472, 24752, 34272, 46512, 62016, 81396, 105336, 134596, 170016, 212520, 263120, 322920, 393120, 475020, 570024, 679644, 805504, 949344, 1113024, 1298528, 1507968, 1743588, 2007768, 2303028
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OFFSET
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0,5
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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FORMULA
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G.f.: 4*x^4/(1-x)^6.
a(n) = n*binomial(n,4)-binomial(n,5) = 4*binomial(n+1,5) = 4*A000389(n+1).
a(n) = 2*A177747(2n-7) with A177747(-7)=A177747(-5)=A177747(-3)=A177747(-1)=0.
(n-4)*a(n) = (n+1)*a(n-1).
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EXAMPLE
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The following sequences are provided by the formula
n*binomial(n,k)-binomial(n,k+1) = k*binomial(n+1,k+1):
. A000217(n) for k=1,
. A007290(n+1) for k=2,
. A050534(n) for k=3,
. a(n) for k=4,
. A000910(n+1) for k=5.
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MATHEMATICA
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LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 0, 0, 4, 24}, 39]
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PROG
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(MAGMA) [4*Binomial(n+1, 5): n in [0..38]];
(Maxima) makelist(coeff(taylor(4*x^4/(1-x)^6, x, 0, n), x, n), n, 0, 38);
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CROSSREFS
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Cf. A000217, A000910, A007290, A050534; A000389, A177747.
First differences are in A033488.
Sequence in context: A069145 A211071 A212135 * A005561 A061612 A097875
Adjacent sequences: A210566 A210567 A210568 * A210570 A210571 A210572
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Mar 23 2012
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STATUS
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approved
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