# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a076037 Showing 1-1 of 1 %I A076037 #6 Mar 30 2012 16:49:31 %S A076037 1,1,1,1,1,1,1,1,2,2,1,1,3,5,5,1,1,4,10,14,14,1,1,5,17,35,42,42,1,1,6, %T A076037 26,74,126,132,132,1,1,7,37,137,326,462,429,429,1,1,8,50,230,726,1446, %U A076037 1716,1430,1430,1,1,9,65,359,1434,3858,6441,6435,4862,4862,1,1,10,82 %N A076037 Square array read by antidiagonals in which row n has g.f. (1-(n-1)*x*C)/(1-n*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. for Catalan numbers A000108. %e A076037 Array begins %e A076037 1 1 1 2 5 14 42 ... (n=0) %e A076037 1 1 2 5 14 42 132 ... (n=1) %e A076037 1 1 3 10 35 126 ... (n=2) %e A076037 1 1 4 17 74 326 ... %o A076037 (PARI) C(x)=(1/2-1/2*(1-4*x)^(1/2))/x; D(x)=(1-(m-1)*x*C(x))/(1-m*x*C(x)); for(i=0,15, forstep(m=i,0,-1,print1(polcoeff(D(x),i-m),","));print()) (Klasen) %Y A076037 Rows give A000108, A000108, A001700, A049027, A076025, A076026. Cf. A076038, A067347. %K A076037 nonn,tabl %O A076037 0,9 %A A076037 _N. J. A. Sloane_, Oct 29 2002 %E A076037 More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Jan 12 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE