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Search: id:A064306
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| A064306 |
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Convolution of A052701 (Catalan numbers multiplied by powers of 2) with powers of -1. |
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+0
5
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| 1, 1, 7, 33, 191, 1153, 7295, 47617, 318463, 2170881, 15028223, 105365505, 746651647, 5339185153, 38478839807, 279201841153, 2037998419967, 14954803494913, 110255315877887, 816299567480833, 6066679566041087
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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W. Lang, On polynomials related to derivatives of the generating function of Catalan numbers, Fib. Quart. 40,4 (2002) 299-313; Eq.(31) with lambda=-1/2.
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FORMULA
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a(n)= ((-1)^n)*sum(C(k)/(-1/2)^k, k=0..n) with C(k)=A000108(k) (Catalan).
a(n)= -a(n-1) +C(n)*2^n, n >= 0, a(-1) := 0, with C(n)=A000108(n).
G.f.: A(2*x)/(1+x), with A(x) g.f. of Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A155603 A054256 A085636 this_sequence A001795 A117663 A063166
Adjacent sequences: A064303 A064304 A064305 this_sequence A064307 A064308 A064309
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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), Sep 13 2001
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