A182736 Sum of parts in all partitions of 2n that do not contain 1 as a part.

0, 2, 8, 24, 56, 120, 252, 476, 880, 1584, 2740, 4620, 7680, 12428, 19824, 31170, 48224, 73678, 111384, 166364, 246120, 360822, 524216, 755504, 1080912, 1535050, 2165592, 3036096, 4230632, 5861828, 8078820, 11076362, 15112384, 20523492, 27747128

Offset: 0

Author

Omar E. Pol, Dec 03 2010

Keywords

• nonn

Comments

Essentially this is a bisection (even indices) of A138880.

Links

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

Crossrefs

Cf. A135010, A138121, A138880, A182734, A182742.

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,2*n)[2]:
seq(a(n), n=0..34); # Alois P. Heinz, Dec 03 2010

Mathematica

b[n_] := (PartitionsP[n] - PartitionsP[n-1])*n; a[n_] := b[2n]; Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Oct 07 2015 *)

Formula

a(n) = 2*n*A182746(n). - Omar E. Pol, Dec 05 2010

Extensions

More terms from Alois P. Heinz, Dec 03 2010