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Search: id:A117186
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| A117186 |
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Expansion of (1+x)c(x^2)/((1-xc(x^2))*sqrt(1-4x^2)), c(x) the g.f. of A000108. |
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+0
3
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| 1, 2, 5, 9, 21, 38, 86, 157, 349, 642, 1410, 2610, 5682, 10572, 22860, 42717, 91869, 172298, 368906, 694054, 1480486, 2793012, 5938740, 11230834, 23813746, 45131348, 95462996, 181268292, 382594884, 727747608, 1533053976
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums of triangle A117184.
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FORMULA
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G.f.: (1+x)(sqrt(1-4x^2)+2x-1)/(2x(1-2x)*sqrt(1-4x^2)); a(n)=sum{k=0..n, C(n+1,(n+k)/2+1)(1+(-1)^(n-k))/2+C(n,(n+k)/2+1/2)(1-(-1)^(n-k))/2}.
G.f.: (1+x)(1+2x-sqrt(1-4x^2))/(2x(1-4x^2)); a(n)=(3*2^n-binomial(2*floor((n+1)/2),floor((n+1)/2)))/2; - Paul Barry (pbarry(AT)wit.ie), Jan 20 2008
Conjecture: a(n)=A058622(n)+A058622(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 21 2008]
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CROSSREFS
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Sequence in context: A030137 A105309 A097163 this_sequence A155042 A001851 A024822
Adjacent sequences: A117183 A117184 A117185 this_sequence A117187 A117188 A117189
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 01 2006
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