A098133 Number of compositions of n in which the smallest part is equal to the number of parts.

1, 0, 0, 1, 2, 2, 2, 2, 3, 5, 8, 11, 14, 17, 20, 24, 30, 39, 52, 69, 90, 115, 144, 177, 215, 260, 315, 384, 472, 584, 725, 900, 1114, 1372, 1679, 2041, 2466, 2965, 3553, 4250, 5082, 6081, 7285, 8738, 10490, 12597, 15121, 18130, 21699, 25912, 30865, 36670

Offset: 1

Author

Vladeta Jovovic, Sep 27 2004

Keywords

• easy
• nonn

Examples

			a(9)=3 because we have [2,7], [7,2] and [3,3,3].
		

Links

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

Crossrefs

Cf. A006141.

Programs

Maple

G:=sum((x^(m^2)-x^(m*(m+1)))/(1-x)^m,m=1..35):Gser:=series(G,x=0,60): seq(coeff(Gser,x^n),n=1..58); # Emeric Deutsch, Apr 18 2005
# second Maple program:
b:= proc(n, s, c) option remember; `if`(s b(n$2, 0):
seq(a(n), n=1..52);  # Alois P. Heinz, Oct 01 2021

Mathematica

b[n_, s_, c_] := b[n, s, c] = If[s < c, 0, If[n == 0,
     If[s == c, 1, 0], Sum[b[n - j, Min[j, s], c + 1], {j, 1, n}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 1, 52}] (* Jean-François Alcover, Mar 13 2022, after Alois P. Heinz *)

Formula

G.f.: Sum_{m>=1} (x^(m^2) - x^(m*(m+1)))/(1-x)^m.

Extensions

More terms from Emeric Deutsch, Apr 18 2005