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A084782
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G.f.: A(x) = 1 + x*A(x)^2/(1-x-x^2).
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0
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1, 1, 3, 11, 42, 168, 696, 2965, 12915, 57276, 257787, 1174597, 5407854, 25119663, 117579351, 554053049, 2626184688, 12513029640, 59898952650, 287931365692, 1389297316104, 6726449251539, 32668497856323, 159114598216251
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vladimir Kruchinin, Compositae and their properties , arXiv:1103.2582
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FORMULA
| a(0)=a(1)=1, for n>1: a(n)=sum (sum a(i)a(j-i)), (i=0, .., j))F(n-j), (j=0, .., n), where F(n) are the Fibonacci numbers A000045 - Mario Catalani (mario.catalani(AT)unito.it), Jun 18 2003
a(n)=sum(sum(binomial(i,n-k-i)*binomial(k+i-1,k-1),i,ceiling((n-k)/2),n-k)*C(k),k,1,n), C(k) - Catalan numbers A000108. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 15 2010]
G.f.: 1/(1-z/(1-z/(1-z/(...)))) where z=x/(1-x-x^2) (continued fraction); more generally g.f. C(x/(1-x-x^2)) where C(x) is the g.f. for the Catalan numbers (A000108). [Joerg Arndt, Mar 18 2011]
G.f.: 2/(sqrt((x^2+5*x-1)/(x^2+x-1))+1) [From Vladimir Kruchinin, Oct 11 2011]
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PROG
| (Other) a(n):=sum(sum(binomial(i, n-k-i)*binomial(k+i-1, k-1), i, ceiling((n-k)/2), n-k)*1/(k+1)*binomial(2*k, k), k, 1, n) (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 15 2010]
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CROSSREFS
| Sequence in context: A143464 A117641 A200030 * A149068 A151088 A149069
Adjacent sequences: A084779 A084780 A084781 * A084783 A084784 A084785
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 14 2003
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