A320818 Number of partitions of n with exactly five sorts of part 1 which are introduced in ascending order.

1, 15, 141, 1066, 7108, 43747, 255045, 1431320, 7814385, 41804990, 220266447, 1147232914, 5922585396, 30367092789, 154877631181, 786633449995, 3982378528296, 20109428513990, 101339359244739, 509871884291730, 2562078441467318, 12861324297841420

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1433

Formula

a(n) = A320736(n) - A320735(n).

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
    end:
a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(5):
seq(a(n), n=5..35);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, k}], Sum[b[n - i*j, i - 1, k], {j, 0, n/i}]];
a[n_] := With[{k = 5}, b[n, n, k] - b[n, n, k - 1]];
a /@ Range[5, 35] (* Jean-François Alcover, Dec 17 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A292746.

Cf. A320735, A320736.

Sequence in context: A346920 A215765 A055903 * A026859 A096046 A093117

Adjacent sequences: A320815 A320816 A320817 * A320819 A320820 A320821

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2018

Status

approved