Alois P. Heinz, <a href="/A183558/b183558_1.txt">Table of n, a(n) for n = 0..5000</a>

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Alois P. Heinz, <a href="/A183558/b183558_1.txt">Table of n, a(n) for n = 10..10005000</a>

First column Column k=1 of A183568.

a:= n-> (l-> l[2])(b(n, n)$2)[2]:

seq(a(n), n=10..50);

a(0) = 0 prepended by Gus Wiseman, Apr 19 2019

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a(0) = 0 added prepended by Gus Wiseman, Apr 19 2019

0, 1, 1, 2, 3, 6, 7, 13, 16, 25, 33, 49, 61, 90, 113, 156, 198, 269, 334, 448, 556, 726, 902, 1163, 1428, 1827, 2237, 2817, 3443, 4302, 5219, 6478, 7833, 9632, 11616, 14197, 17031, 20712, 24769, 29925, 35688, 42920, 50980, 61059, 72318, 86206, 101837, 120941

1,3

0,4

max = 50; f = (1 - Product[1 - x^j + x^(2*j), {j, 1, max}])/Product[1 - x^j, {j, 1, max}]; s = Series[f, {x, 0, max}]; CoefficientList[s, x] // Rest (* Jean-François Alcover, Oct 01 2014 . Edited by _Gus Wiseman_, Apr 19 2019 *)

Cf. A052485, A090858, A117571, A127002, A325241, A325242 , , A325244.

a(0) = 0 added by Gus Wiseman, Apr 19 2019

From Gus Wiseman, Apr 19 2019: (Start)

The a(1) = 1 through a(8) = 16 partitions are the following. The Heinz numbers of these partitions are given by A052485 (weak numbers).

(1) (2) (3) (4) (5) (6) (7) (8)

(21) (31) (32) (42) (43) (53)

(211) (41) (51) (52) (62)

(221) (321) (61) (71)

(311) (411) (322) (332)

(2111) (3111) (331) (422)

(21111) (421) (431)

(511) (521)

(2221) (611)

(3211) (3221)

(4111) (4211)

(31111) (5111)

(211111) (32111)

(41111)

(311111)

(2111111)

(End)

Cf. A052485, A090858, A117571, A127002, A325241, A325242 , A325244.

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