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Shifts left when MASKCONVolved with itself.
2

%I #4 Nov 11 2010 07:34:06

%S 1,1,2,4,12,24,72,192,720,1440,4320,11520,43200,103680,362880,1105920,

%T 4665600,9331200,27993600,74649600,279936000,671846400,2351462400,

%U 7166361600,30233088000,67184640000,221709312000,644972544000

%N Shifts left when MASKCONVolved with itself.

%C Note that the factorials 1!, 2!, 4!, 6!, 9! can be found from the positions 1,3,6,9,15 (or 2,4,7,10,16 if zero-based indexing is used) of this sequence. I do not know whether any larger factorials occur in the sequence.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%p EIGENbyMASKCONV := proc(upto_n) local n,a,j,i,s,m; a := [1]; for i from 0 to upto_n do s := 0; m := maskees(i); n := nops(m); for j from 1 to n do s := s+(a[m[j]+1]*a[m[(n-j)+1]+1]); od; a := [op(a),s]; od; RETURN(a); end;

%p maskees := proc(n) local a,b,u,i; a := []; b := list_mask_bits(n); u := (2^nops(b))-1; for i from 0 to u do a := [op(a),sum_by_mask_list(i,b)]; od; RETURN(a); end;

%p list_mask_bits := proc(nn) local n,a,x; n := nn; x := 1; a := []; while(n > 0) do if(1 = (n mod 2)) then a := [op(a),x]; fi; n := floor(n/2); x := 2*x; od; RETURN(a); end;

%p sum_by_mask_list := proc(nn,a) local n,i,s; n := nn; s := 0; i := 1; while(n > 0) do if(1 = (n mod 2)) then s := s + a[i]; fi; n := floor(n/2); i := i+1; od; RETURN(s); end;

%Y Other self-convolved sequences: A000108, A007460 - A007464, A025192, A038044, A061922.

%K nonn,eigen

%O 0,3

%A Antti Karttunen, Jun 12 2001