A243737 - OEIS

%I #9 Feb 10 2015 04:00:17

%S 1,0,1,3,7,13,25,46,89,175,351,710,1443,2926,5920,11936,23987,48072,

%T 96139,191977,382992,763686,1522581,3035979,6055454,12082887,24120923,

%U 48174935,96259627,192418152,384772810,769651514,1539889604,3081525905,6167365392

%N Number of compositions of n with exactly two occurrences of the largest part.

%H Joerg Arndt and Alois P. Heinz, <a href="/A243737/b243737.txt">Table of n, a(n) for n = 2..650</a>

%p b:= proc(n, p, i) option remember; `if`(n=0, p!,

%p       `if`(i<1, 0, add(b(n-i*j, p+j, i-1)/j!, j=0..n/i)))

%p     end:

%p a:= proc(n) local k; k:=2;

%p       add(b(n-i*k, k, i-1)/k!, i=1..n/k)

%p     end:

%p seq(a(n), n=2..40);

%t b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_] := (k=2; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]) ; Table[ a[n], {n, 2, 40}] (* _Jean-François Alcover_, Feb 10 2015, after Maple *)

%Y Column k=2 of A238341.

%K nonn

%O 2,4

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 09 2014