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A182737 Sum of parts in all partitions of 2n+1 that do not contain 1 as a part.

%I A182737 #18 Nov 11 2015 10:36:58
%S A182737 0,3,10,28,72,154,312,615,1122,1995,3465,5819,9575,15498,24563,38378,
%T A182737 59202,90055,135420,201630,297045,433741,628155,902212,1286348,
%U A182737 1821567,2562126,3581655,4977867,6879400,9457318,12936609,17610320,23863323,32196090
%N A182737 Sum of parts in all partitions of 2n+1 that do not contain 1 as a part.
%C A182737 Bisection (odd part) of A138880.
%H A182737 Alois P. Heinz, <a href="/A182737/b182737.txt">Table of n, a(n) for n = 0..1000</a>
%F A182737 a(n) = A005408(n)*A182747(n).
%p A182737 b:= proc(n,i) option remember; local p,q;
%p A182737       if n<0 then [0,0]
%p A182737     elif n=0 then [1,0]
%p A182737     elif i<2 then [0,0]
%p A182737     else p, q:= b(n,i-1), b(n-i,i);
%p A182737         [p[1]+q[1], p[2]+q[2]+q[1]*i]
%p A182737       fi
%p A182737     end:
%p A182737 a:= n-> b(2*n+1,2*n+1)[2]:
%p A182737 seq(a(n), n=0..34); # _Alois P. Heinz_, Dec 03 2010
%t A182737 b[n_, i_] := b[n, i] = Module[{p, q}, Which[n<0, {0, 0}, n == 0, {1, 0}, i<2, {0, 0}, True, {p, q} = {b[n, i-1], b[n-i, i]}; {p[[1]] + q[[1]], p[[2]] + q[[2]] + q[[1]]*i}]]; a[n_] := b[2*n + 1, 2*n+1][[2]]; Table[ a[n], {n, 0, 34}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)
%Y A182737 Cf. A135010, A138121, A138880, A182736, A182743.
%K A182737 nonn
%O A182737 0,2
%A A182737 _Omar E. Pol_, Dec 03 2010
%E A182737 More terms from _Alois P. Heinz_, Dec 03 2010