A098716 - OEIS

%I #12 May 28 2024 09:39:17

%S 1,1,2,5,13,49,169,972,5559,52979,526450,10617149,214475363,

%T 9035782113,476715641982,51820049305123,7479565064189887,

%U 2645418340373829359,1318520401609595443835,1774758704783778068230273

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

%e 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.

%p 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

%t a[n_] := SeriesCoefficient[1/Product[1 - x^j, {j, 1, PartitionsP[n - 1]}], {x, 0, PartitionsP[n]}];

%t Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, May 28 2024, after _Emeric Deutsch_ *)

%Y Cf. A058699.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Sep 29 2004

%E More terms from _Emeric Deutsch_, Apr 23 2006