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A014432
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a(n) = Sum( a(i)a(n-1-i),{i,1,n-1} ), with a(0) = 1, a(1) = 3.
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3
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1, 3, 3, 12, 30, 111, 363, 1353, 4917, 18777, 71769, 280506, 1103556, 4395009, 17622309, 71220828, 289510662, 1183627137, 4862148753, 20061888924, 83100910530, 345457823493, 1440734205513, 6026408186457, 25275954499905, 106277040064191
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1+x-sqrt(1-2*x-11*x^2))/2 - Michael Somos, Jun 08, 2000.
A014432(n) = (3/(11*n)) * ((3+n)*A025237(n+1) - (2*n+3)*A025237(n)) for n>0 [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 02 2010]
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MAPLE
| seq(coeff(convert(series((1+x-sqrt(1-2*x-11*x^2))/(2*x), x, 50), polynom), x, i), i=0..30); A014431:=proc(n) options remember: local i: if n<2 then RETURN([1, 3][n+1]) else RETURN(add(A014431(i)*A014431(n-1-i), i=1..n-1)) fi:end; seq(A014431(n), n=0..30); (C. Ronaldo)
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PROG
| (PARI) a(n)=polcoeff((1+x-sqrt(1-2*x-11*x^2+x*O(x^n)))/2, n)
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CROSSREFS
| Cf. A025237.
Sequence in context: A161804 A097342 A025236 * A107330 A076509 A206704
Adjacent sequences: A014429 A014430 A014431 * A014433 A014434 A014435
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KEYWORD
| nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
| Corrected by C. Ronaldo (aga_new_ac(AT)hotmail.com) and Ralf Stephan, Dec 19 2004
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