A134050 - OEIS

%I #7 Jun 25 2016 11:41:59

%S 1,1,3,23,512,34939,7637688,5539372954,13703105571256,

%T 118149647382446899,3611029954044991125872,

%U 396437704741571722701763726,158000007601023255711816905096600,230573407734730856178976755626889887934,1240859469782266733203067689710529642528338320,24774501349228223607795736923546381007921447933762900,1844552309599593759846481462075800633418691335116469275638832,514424614172853969912935745275645969935778834184491996786063734076739

%N Column 0 of triangle A134049.

%C Related to binary partitions.

%C It appears that, for n>1, a(n) is odd iff n = 2^k+1 for k>=0.

%H Paul D. Hanna, <a href="/A134050/b134050.txt">Table of n, a(n) for n = 0..40</a>

%e Triangle T=A134049 has the following properties:

%e (1) [T^(2^m)](n,k) = T(n+m,k+m)/(2^m)^(n-k) for m>=0; and

%e (2) [T^( 1/2^(n-1) )](n,k) = (2^k)^(n-k) for n>=k>=0.

%o (PARI) {a(n)=local(M=Mat(1),L,R);for(i=1,n, L=sum(j=1,#M,-(M^0-M)^j/j);M=sum(j=0,#L,(L/2^(#L-1))^j/j!); R=matrix(#M+1,#M+1,r,c,if(r>=c,if(r<=#M,M[r,c],2^((c-1)*(#M+1-c))))); M=R^(2^(#R-2)) );M[n+1,1]}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A134049; columns: A134051, A134052, A134053; A134054 (row sums).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 04 2007