A098716 Number of partitions of the n-th partition number into integers not greater than the (n-1)-th partition number.

1, 1, 2, 5, 13, 49, 169, 972, 5559, 52979, 526450, 10617149, 214475363, 9035782113, 476715641982, 51820049305123, 7479565064189887, 2645418340373829359, 1318520401609595443835, 1774758704783778068230273

Offset

1,3

Links

Table of n, a(n) for n=1..20.

Example

n=7: A000041(7)=15 has A000041(15)=176 partitions, seven of them with integers greater than A000041(7-1)=11: 12+3, 12+2+1, 12+1+1, 13+2, 13+1+1, 14+1 and 15, therefore a(7)=176-7=169.

Maple

with(combinat): a:=proc(n) local G, Gser: G:=1/product(1-x^j, j=1..numbpart(n-1)): Gser:=series(G, x=0, 20+numbpart(n)): coeff(Gser, x^numbpart(n)) end: seq(a(n), n=1..22); # Emeric Deutsch, Apr 23 2006

Crossrefs

Cf. A058699.

Sequence in context: A212821 A067021 A269068 * A082938 A303792 A059103

Adjacent sequences: A098713 A098714 A098715 * A098717 A098718 A098719

Keyword

nonn

Author

Reinhard Zumkeller, Sep 29 2004

Extensions

More terms from Emeric Deutsch, Apr 23 2006

Status

approved