A079281 Number of compositions of 2^n into distinct parts.

1, 1, 3, 19, 435, 74875, 348317763, 294729601581739, 682404222981720262704195, 298417646219775679438413815505895285915, 13661663328896434876017827688479176004409461863714010289523203

Offset: 0

Author

Henry Bottomley, Feb 08 2003

Keywords

• nonn

Examples

			a(2) = 3 since the compositions of 2^2=4 into distinct parts are 4, 3+1 and 1+3.
		

Links

• Henry Bottomley, Partition and composition calculator using a Java applet
• Index entries for sequences related to compositions

Crossrefs

Cf. A058891 (offset for compositions of 2^n), A067735, A068413.

Programs

Maple

b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;
      `if`(n=m, x^i, `if`(n>m, 0,
       expand(b(n, i-1)+`if`(i>n, 0, x*b(n-i, i-1)))))
    end:
a:= n->(p->add(coeff(p, x, i)*i!, i=0..degree(p)))(b(2^n$2)):
seq(a(n), n=0..9); # Alois P. Heinz, Apr 27 2014

Mathematica

b[n_, i_] := b[n, i] = With[{ m = i*(i+1)/2}, If[n==m, x^i, If[n>m, 0, Expand[b[n, i-1] + If[i>n, 0, x*b[n-i, i-1]]]]]]; a[n_] := Function[{p}, Sum[Coefficient[p, x, i]*i!, {i, 0, Exponent[p, x]}]][b[2^n, 2^n]]; Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Oct 05 2015, after Alois P. Heinz *)

Formula

a(n) = A032020(A000079(n)).