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

%I A171985 #9 Feb 16 2017 02:30:52
%S A171985 1,2,5,11,23,44,82,146,252,423,695,1116,1763,2738,4192,6334,9459,
%T A171985 13968,20425,29588,42496,60547,85628,120246,167762,232605,320635,
%U A171985 439544,599412,813360,1098480,1476870,1977087,2635869,3500382,4630932,6104533,8019131,10499093
%N A171985 Number of partitions of 2*n-1 into parts not greater than n.
%C A171985 Central terms of the triangle in A026820: a(n)=A026820(2*n-1,n).
%H A171985 Alois P. Heinz, <a href="/A171985/b171985.txt">Table of n, a(n) for n = 1..1000</a>
%e A171985 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.
%p A171985 g:= proc(n, i) option remember;
%p A171985      `if`(n=0, 1, `if`(i>1, g(n, i-1), 0)+`if`(i>n, 0, g(n-i, i)))
%p A171985     end:
%p A171985 a:= n-> g(2*n-1, n):
%p A171985 seq (a(n), n=1..40);  # _Alois P. Heinz_, Jul 18 2012
%t A171985 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_ *)
%K A171985 nonn
%O A171985 1,2
%A A171985 _Reinhard Zumkeller_, Jan 21 2010