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A171985 Number of partitions of 2*n-1 into parts not greater than n. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 16 2017, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A124920 A064934 A227637 * A005986 A277828 A147878

Adjacent sequences:  A171982 A171983 A171984 * A171986 A171987 A171988

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 21 2010

STATUS

approved

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Last modified April 25 21:06 EDT 2019. Contains 322461 sequences. (Running on oeis4.)