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A320817
Number of partitions of n with exactly four sorts of part 1 which are introduced in ascending order.
2
1, 10, 66, 361, 1778, 8207, 36310, 156095, 657785, 2733065, 11241497, 45900679, 186420826, 754165809, 3042167236, 12245294090, 49211278321, 197535872510, 792216674789, 3175088068035, 12719020008668, 50932090504830, 203896407951944, 816089798651203
OFFSET
4,2
LINKS
FORMULA
a(n) = A320735(n) - A320734(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))(4):
seq(a(n), n=4..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 = 4}, b[n, n, k] - b[n, n, k-1]];
a /@ Range[4, 35] (* Jean-François Alcover, Dec 17 2020, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A292746.
Sequence in context: A024391 A074362 A080421 * A004310 A026853 A177452
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 21 2018
STATUS
approved