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

0, 3, 10, 28, 72, 154, 312, 615, 1122, 1995, 3465, 5819, 9575, 15498, 24563, 38378, 59202, 90055, 135420, 201630, 297045, 433741, 628155, 902212, 1286348, 1821567, 2562126, 3581655, 4977867, 6879400, 9457318, 12936609, 17610320, 23863323, 32196090

Offset: 0

Author

Omar E. Pol, Dec 03 2010

Keywords

• nonn

Comments

Bisection (odd part) of A138880.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A135010, A138121, A138880, A182736, A182743.

Programs

Maple

b:= proc(n,i) option remember; local p,q;
      if n<0 then [0,0]
    elif n=0 then [1,0]
    elif i<2 then [0,0]
    else p, q:= b(n,i-1), b(n-i,i);
        [p[1]+q[1], p[2]+q[2]+q[1]*i]
      fi
    end:
a:= n-> b(2*n+1,2*n+1)[2]:
seq(a(n), n=0..34); # Alois P. Heinz, Dec 03 2010

Mathematica

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 *)

Formula

a(n) = A005408(n)*A182747(n).

Extensions

More terms from Alois P. Heinz, Dec 03 2010