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

1,2

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Sequence in context: A124920 A064934 A227637 * A354044 A005986 A333396

Adjacent sequences: A171982 A171983 A171984 * A171986 A171987 A171988

Keyword

nonn

Author

Reinhard Zumkeller, Jan 21 2010

Status

approved