cp's OEIS Frontend

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

%I A079281 #16 Oct 05 2015 11:20:58
%S A079281 1,1,3,19,435,74875,348317763,294729601581739,
%T A079281 682404222981720262704195,298417646219775679438413815505895285915,
%U A079281 13661663328896434876017827688479176004409461863714010289523203
%N A079281 Number of compositions of 2^n into distinct parts.
%H A079281 Henry Bottomley, <a href="http://www.se16.info/js/partitionstest.htm">Partition and composition calculator using a Java applet</a>
%H A079281 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A079281 a(n) = A032020(A000079(n)).
%e A079281 a(2) = 3 since the compositions of 2^2=4 into distinct parts are 4, 3+1 and 1+3.
%p A079281 b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;
%p A079281       `if`(n=m, x^i, `if`(n>m, 0,
%p A079281        expand(b(n, i-1)+`if`(i>n, 0, x*b(n-i, i-1)))))
%p A079281     end:
%p A079281 a:= n->(p->add(coeff(p, x, i)*i!, i=0..degree(p)))(b(2^n$2)):
%p A079281 seq(a(n), n=0..9); # _Alois P. Heinz_, Apr 27 2014
%t A079281 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_ *)
%Y A079281 Cf. A058891 (offset for compositions of 2^n), A067735, A068413.
%K A079281 nonn
%O A079281 0,3
%A A079281 _Henry Bottomley_, Feb 08 2003