A061922 Xcatalans - produced as a self-convolved sequence like Catalan numbers (A000108) but use carryless GF(2)[ X ] polynomial multiplication.

1, 1, 2, 5, 14, 42, 132, 421, 1382, 4478, 15580, 54114, 181676, 650484, 2289320, 8028901, 28045302, 103229014, 372640460, 1336511110, 4882492452, 17534836812, 63692926552, 234287550818, 868236370364, 3281589811404

Offset: 0

Author

Antti Karttunen, May 15 2001

Keywords

• nonn
• easy
• eigen

Comments

Shifts one place left when Xmult-convolved (XMULTCONV) with itself.

Crossrefs

For Xmult, see A048720 (Xmult table) or A048631 (Xfactorials). Other self-convolved sequences: A000108, A007460 - A007464, A025192.

Programs

Maple

Xcatalans(30); Xcatalans := proc(upto_n) local a,i,k; a := [1]; for i from 1 to upto_n do a := [ op(a), add(Xmult(a[k],a[i-k+1]), k=1..i)]; od; RETURN(a); end;
XMULTCONV := proc(a,b) local c,i,k,n; n := min( nops(a), nops(b) ); c := []; for i from 0 to n-1 do c := [ op(c), add(Xmult(a[k+1],b[i-k+1]), k=0..i)]; od; RETURN(c); end;