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A099327
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Expansion of ((1-x)sqrt(1+2x)+(1+x)sqrt(1-2x))/(2(1-2x)^(5/2)).
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2
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1, 5, 16, 45, 117, 291, 700, 1646, 3799, 8647, 19448, 43330, 95738, 210094, 458216, 994204, 2146955, 4617439, 9893376, 21128058, 44982486, 95510090, 202278376, 427425860, 901236582, 1896594966, 3983929680, 8354539156, 17492095604
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OFFSET
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0,2
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COMMENTS
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The g.f. is transformed to 1/(1-x)^5 under the Chebyshev transformation A(x)->1/(1+x^2)A(x/(1+x^2)). Second binomial transform of the sequence with g.f. 1/c(-x)^3, where c(x) is the g.f. of the Catalan numbers A000108.
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LINKS
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Table of n, a(n) for n=0..28.
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FORMULA
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a(n)=sum{k=0..n, (k+1)binomial(n, (n-k)/2)binomial(k+4, 4)(1+(-1)^(n-k))/(n+k+2)}.
Conjecture: +n*(n-3)*a(n) +2*(-n^2+6)*a(n-1) +4*-(n-1)*(n-5)*a(n-2) +8*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 24 2012
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CROSSREFS
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Cf. A099325, A099326.
Sequence in context: A048777 A185003 A189390 * A004146 A071101 A110580
Adjacent sequences: A099324 A099325 A099326 * A099328 A099329 A099330
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Oct 12 2004
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STATUS
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approved
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