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A306187 Number of n-times partitions of n. 4
1, 1, 3, 10, 65, 371, 3780, 33552, 472971, 5736082, 97047819, 1547576394, 32992294296, 626527881617, 15202246707840, 352290010708120, 9970739854456849, 262225912049078193, 8309425491887714632, 250946978120046026219, 8898019305511325083149 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A k-times partition of n for k > 1 is a sequence of (k-1)-times partitions, one of each part in an integer partition of n. A 1-times partition of n is just an integer partition of n. The only 0-times partition of n is the number n itself. - Gus Wiseman, Jan 27 2019

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..410

FORMULA

a(n) = A323718(n,n).

EXAMPLE

From Gus Wiseman, Jan 27 2019: (Start)

The a(1) = 1 through a(3) = 10 partitions:

  (1)  ((2))     (((3)))

       ((11))    (((21)))

       ((1)(1))  (((111)))

                 (((2)(1)))

                 (((11)(1)))

                 (((2))((1)))

                 (((1)(1)(1)))

                 (((11))((1)))

                 (((1)(1))((1)))

                 (((1))((1))((1)))

(End)

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0 or k=0 or i=1,

      1, b(n, i-1, k)+b(i$2, k-1)*b(n-i, min(n-i, i), k))

    end:

a:= n-> b(n$3):

seq(a(n), n=0..25);

MATHEMATICA

ptnlevct[n_, k_]:=Switch[k, 0, 1, 1, PartitionsP[n], _, SeriesCoefficient[Product[1/(1-ptnlevct[m, k-1]*x^m), {m, n}], {x, 0, n}]];

Table[ptnlevct[n, n], {n, 0, 8}] (* Gus Wiseman, Jan 27 2019 *)

CROSSREFS

Main diagonal of A323718.

Cf. A000041, A306188.

Cf. A001970, A063834, A096752, A196545, A261280, A289501, A290354.

Sequence in context: A237998 A167939 A206724 * A009400 A217388 A004102

Adjacent sequences:  A306184 A306185 A306186 * A306188 A306189 A306190

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 27 2019

STATUS

approved

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Last modified September 16 11:05 EDT 2019. Contains 327095 sequences. (Running on oeis4.)