A171985 Number of partitions of 2*n-1 into parts not greater than n.

1, 2, 5, 11, 23, 44, 82, 146, 252, 423, 695, 1116, 1763, 2738, 4192, 6334, 9459, 13968, 20425, 29588, 42496, 60547, 85628, 120246, 167762, 232605, 320635, 439544, 599412, 813360, 1098480, 1476870, 1977087, 2635869, 3500382, 4630932, 6104533, 8019131, 10499093

Offset: 1

Author

Reinhard Zumkeller, Jan 21 2010

Keywords

• nonn

Comments

Central terms of the triangle in A026820: a(n)=A026820(2*n-1,n).

Examples

			a(4) = (partitions of 7 into parts <= 4) = #{4+3, 4+2+1, 4+1+1+1, 3+3+1, 3+2+2, 3+2+1+1, 3+1+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1} = 11.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Programs

Maple

g:= proc(n, i) option remember;
     `if`(n=0, 1, `if`(i>1, g(n, i-1), 0)+`if`(i>n, 0, g(n-i, i)))
    end:
a:= n-> g(2*n-1, n):
seq (a(n), n=1..40);  # Alois P. Heinz, Jul 18 2012

Mathematica

g[n_, i_] := g[n, i] = If[n==0, 1, If[i>1, g[n, i-1], 0]+If[i>n, 0, g[n-i, i]]]; a[n_] := g[2*n-1, n]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Feb 16 2017, after Alois P. Heinz *)