A134050 Column 0 of triangle A134049.

1, 1, 3, 23, 512, 34939, 7637688, 5539372954, 13703105571256, 118149647382446899, 3611029954044991125872, 396437704741571722701763726, 158000007601023255711816905096600, 230573407734730856178976755626889887934, 1240859469782266733203067689710529642528338320, 24774501349228223607795736923546381007921447933762900, 1844552309599593759846481462075800633418691335116469275638832, 514424614172853969912935745275645969935778834184491996786063734076739

Offset

0,3

Comments

Related to binary partitions.

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

Links

Paul D. Hanna, Table of n, a(n) for n = 0..40

Example

Triangle T=A134049 has the following properties:
(1) [T^(2^m)](n,k) = T(n+m,k+m)/(2^m)^(n-k) for m>=0; and
(2) [T^( 1/2^(n-1) )](n,k) = (2^k)^(n-k) for n>=k>=0.

Prog

(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]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

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

Sequence in context: A268668 A171777 A154896 * A101191 A127900 A229266

Adjacent sequences: A134047 A134048 A134049 * A134051 A134052 A134053

Keyword

nonn

Author

Paul D. Hanna, Oct 04 2007

Status

approved