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A100335
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An inverse Catalan transform of J(2n).
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5
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0, 1, 4, 11, 27, 64, 149, 341, 768, 1707, 3755, 8192, 17749, 38229, 81920, 174763, 371371, 786432, 1660245, 3495253, 7340032, 15379115, 32156331, 67108864, 139810133, 290805077, 603979776, 1252698795, 2594876075, 5368709120
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OFFSET
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0,3
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COMMENTS
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The g.f. is obtained from that of A002450 through the mapping g(x)->g(x(1-x)). A002450 may be retrieved through the mapping g(x)->g(xc(x)), where c(x) is the g.f. of A000108.
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LINKS
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Table of n, a(n) for n=0..29.
Index entries for linear recurrences with constant coefficients, signature (5,-9,8,-4).
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FORMULA
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G.f.: x*(1-x)/(1 - 5x + 9x^2 - 8x^3 + 4x^4);
a(n) = 5*a(n-1) - 9*a(n-2) + 8*a(n-3) - 4*a(n-4);
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^k*(4^(n-k)-1)/3.
a(n) = (1/3)*((n+1)*2^n - A010892(n)). - Ralf Stephan, May 15 2007
Binomial transform of A042965: (1, 3, 4, 5, 7, 8, 9, 11, 12, 13,...), also row sums of triangle A133110. - Gary W. Adamson, Sep 12 2007
a(n) = Sum_{k=0..n} A109466(n,k)*A002450(k). - Philippe Deléham, Oct 30 2008
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CROSSREFS
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Cf. A001045, A100334.
Cf. A133110, A042965.
Sequence in context: A000253 A276691 A047859 * A340228 A080869 A137229
Adjacent sequences: A100332 A100333 A100334 * A100336 A100337 A100338
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Nov 17 2004
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STATUS
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approved
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