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A116880 Generalized Catalan triangle, called CM(1,2). 4
1, 1, 3, 3, 7, 13, 13, 29, 41, 67, 67, 147, 195, 247, 381, 381, 829, 1069, 1277, 1545, 2307, 2307, 4995, 6339, 7379, 8451, 9975, 14589, 14589, 31485, 39549, 45373, 50733, 56829, 66057, 95235, 95235, 205059, 255747, 290691, 320707, 351187, 388099, 446455 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This triangle generalizes the 'new' Catalan triangle A028364 (which could be called CM(1,1); M stands for author Meeussen).

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..2500

W. Lang: First 10 rows.

FORMULA

G.f. for columns m >= 0 (without leading zeros): c(2;x)*Sum_{k=0..m} C(1,2;m,k)*(2*c(2*x))^k with c(2;x):=(1+2*x*c(2*x))/(1+x) the g.f. of A064062 and c(x) is the g.f. of A000108 (Catalan). C(1,2;n,m) is the triangle A115193(n,m).

MAPLE

lim:=8: c:=(1-sqrt(1-8*x))/(4*x): g:=(1+2*x*c)/(1+x): gf1:=g*(x*c)^m: for m from 0 to lim do t:=taylor(gf1, x, lim+1): for n from 0 to lim do a[n, m]:=coeff(t, x, n):od:od: gf2:=g*sum(a[s, k]*(2*c)^k, k=0..s): for s from 0 to lim do t:=taylor(gf2, x, lim+1): for n from 0 to lim do b[n, s]:=coeff(t, x, n):od:od: seq(seq(b[n-s, s], s=0..n), n=0..lim); # Nathaniel Johnston, Apr 30 2011

CROSSREFS

Row sums give A116881.

Sequence in context: A219211 A088859 A177942 * A051123 A096188 A187873

Adjacent sequences:  A116877 A116878 A116879 * A116881 A116882 A116883

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Mar 24 2006

STATUS

approved

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Last modified March 6 20:37 EST 2021. Contains 341850 sequences. (Running on oeis4.)