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Revision History for A117505

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Triangle of coefficients for polynomials used for the column g.f.s of triangle A116880, called CM(1,2).
(history; published version)

#8 by Wolfdieter Lang at Fri Aug 30 04:09:24 EDT 2019

STATUS

editing

approved

#7 by Wolfdieter Lang at Fri Aug 30 04:09:20 EDT 2019

LINKS

W. Lang: <a href="/LANGCHANGE/A117505/a117505.texttxt">First 10 rows.</a>

STATUS

approved

editing

#6 by N. J. A. Sloane at Wed Aug 28 09:25:23 EDT 2019

LINKS

W. Lang: <a href="http://www.itp.kit.edu/~wl/EISpubLANGCHANGE/A117505.text">First 10 rows.</a>

Discussion

Wed Aug 28

09:25

OEIS Server: https://oeis.org/edit/global/2824

#5 by Charles R Greathouse IV at Thu Jul 09 17:57:10 EDT 2015

LINKS

W. Lang: <a href="http://www-.itp.physik.uni-karlsruhekit.deedu/~wl/EISpub/A117505.text">First 10 rows.</a>

Discussion

Thu Jul 09

17:57

OEIS Server: https://oeis.org/edit/global/2449

#4 by Russ Cox at Sat Mar 31 13:20:12 EDT 2012

AUTHOR

_Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), _, Apr 13 2006

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/878

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

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).

KEYWORD

nonn,easy,tabl,new

#2 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

FORMULA

a(m,m)= A064062(m) =:C(2;m), m>=0, and a(m,k)=2*A110507A052701(k) = C(k)*2^(k+1), for k=1,...,m-1, and C(k):=A000108(k) (Catalan).

KEYWORD

nonn,easy,tabl,new

#1 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

NAME

Triangle of coefficients for polynomials used for the column g.f.s of triangle A116880, called CM(1,2).

DATA

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

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

W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A117505.text">First 10 rows.</a>

FORMULA

a(m,m)= A064062(m) =:C(2;m), m>=0, and a(m,k)=2*A110507(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).

KEYWORD

nonn,easy,tabl,new

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 13 2006

STATUS

approved