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A085139
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a(0)=1, for n>0: a(n)=(1/2) Sum( Sum( a(j)a(i-j), (j=0..i)) (1+(-1)^(n+1+i)), (i=0..n)).
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0
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1, 1, 2, 6, 18, 58, 194, 670, 2370, 8546, 31298, 116102, 435346, 1647418, 6283394, 24130174, 93226242, 362098050, 1413098370, 5538138182, 21788069266, 86016385274, 340655956802, 1353023683486, 5388230857538, 21510345134178
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: A(x)=(1/(2x))(1 - x^2 - Sqrt[(1 - x^2)^2 - 4x(1 - x^2)])
G.f.: c(x/(1-x^2)) where c(x) is the g.f. of A000108. - Paul Barry (pbarry(AT)wit.ie), Apr 12 2005
G.f.: 1/(1-z/(1-z/(1-z/(...)))) where z=x/(1-x^2) (continued fraction); this is a special case of the previous formula. [Joerg Arndt, Mar 18 2011]
a(n)=sum{k=0..floor(n/2), C(n-k,k)C(n-2k)}-sum{k=0..,floor((n-2)/2), C(n-k-2,k)C(n-2k-2)}; [From Paul Barry (pbarry(AT)wit.ie), Nov 30 2008]
Contribution from Paul Barry (pbarry(AT)wit.ie), May 27 2009: (Start)
G.f.: 1+x/(1-2x-2x^2/(1-x-2x^2/(1-2x-x^2/(1-2x-2x^2/(1-x-2x^2/(1-2x-x^2/(1-2x-2x^2/(1-x-2x^2/(1-... (continued fraction).
a(n)=0^n+sum{k=0..floor((n-1)/2), C(n-k-1,k)*A000108(n-2k)}. (End)
G.f.: M(F(x))) where F(x) is the g.f. of A000045, M(x) is the g.f. A001006 [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 06 2010]
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MATHEMATICA
| a[n_] := a[n] = (1/2)Sum[Sum[a[j]a[i -j], {j, 0, i}](1 + (-1)^(n+1+i)), {i, 0, n}]; a[0] = 1; Table[a[n], {n, 0, 10}]
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CROSSREFS
| Sequence in context: A151282 A193777 A157004 * A150041 A190790 A150042
Adjacent sequences: A085136 A085137 A085138 * A085140 A085141 A085142
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Jun 20 2003
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