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Search: id:A117505
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| A117505 |
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Triangle of coefficients for polynomials used for the column g.f.s of triangle A116880, called CM(1,2). |
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1
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| 1, 2, 1, 2, 4, 3, 2, 4, 16, 13, 2, 4, 16, 80, 67, 2, 4, 16, 80, 448, 381, 2, 4, 16, 80, 448, 2688, 2307, 2, 4, 16, 80, 448, 2688, 16896, 14589, 2, 4, 16, 80, 448, 2688, 16896, 109824, 95235, 2, 4, 16, 80, 448, 2688
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The g.f. G(m,x) for column m=1,2,... of triangle A116880=CM(1,2) is x*(-sum(a(m,k)*x^(k-1),k=1..m) + sum(a(m,k)*x^k,k=0..m)*2*c(2*x))/(1+x), with the o.g.f. c(x) of A000108 (Catalan numbers).
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LINKS
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W. Lang: First 10 rows.
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FORMULA
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a(m,m)= A064062(m) =:C(2;m), m>=0, and a(m,k)=2*A052701(k) = C(k)*2^(k+1), for k=1,...,m-1, and C(k):=A000108(k) (Catalan).
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EXAMPLE
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m=3: G(3,x)= x*(-(4+16*x+13*x^2) +
(2+4*x+16*x^2+13*x^3)*2*c(2*x))/(1+x).
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CROSSREFS
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Sequence in context: A078142 A133422 A099312 this_sequence A131380 A100461 A124904
Adjacent sequences: A117502 A117503 A117504 this_sequence A117506 A117507 A117508
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 13 2006
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