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A117505 Triangle of coefficients for polynomials used for the column g.f.s of triangle A116880, called CM(1,2). 1
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; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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).
LINKS
FORMULA
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).
EXAMPLE
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).
CROSSREFS
Sequence in context: A133422 A331136 A099312 * A331499 A209128 A209131
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Apr 13 2006
STATUS
approved

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Last modified April 23 12:27 EDT 2024. Contains 371912 sequences. (Running on oeis4.)