

A103650


G.f.: x^2/((1x^2)^2*Product_{i>0}(1x^i)).


3



0, 1, 1, 4, 5, 12, 16, 31, 42, 72, 98, 155, 210, 315, 423, 610, 812, 1136, 1498, 2047, 2674, 3585, 4642, 6125, 7865, 10240, 13046, 16791, 21237, 27060, 33993, 42933, 53591, 67155, 83332, 103687, 127956, 158196, 194217, 238720, 291663, 356582
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OFFSET

1,4


COMMENTS

Let pi be a partition of n and b(pi,k) = Sum p, where p runs over all distinct parts p of pi whose multiplicities are >=k. Let T(n,k) = Sum b(pi,k), when pi runs over all partitions pi of n. G.f. for T(n,k) is x^k/((1x^k)^2*Product_{i>0}(1x^i)). a(n) = T(n,2).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..500


FORMULA

a(n) = Sum_{k>0} k * A264404(n,k).  Alois P. Heinz, Nov 29 2015
For n>2, a(n) is the Euler transform of [1,3,1,1,1,1,...].  Benedict W. J. Irwin, Jul 29 2016
a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n/3)) / (8*Pi^2).  Vaclav Kotesovec, Jul 30 2016


EXAMPLE

Partitions of 4 are [1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4] and a(4) = 1 + 1 + 2 + 0 + 0 = 4.


MATHEMATICA

Drop[ CoefficientList[ Series[ x^2/((1  x^2)^2*Product[(1  x^i), {i, 50}]), {x, 0, 42}], x], 1] (* Robert G. Wilson v, Mar 29 2005 *)
Table[Sum[PartitionsP[k]*(nk)*(1 + (1)^(nk))/4, {k, 0, n}], {n, 1, 50}] (* Vaclav Kotesovec, Jul 30 2016 *)


CROSSREFS

Cf. A014153.
Sequence in context: A115375 A212114 A269227 * A131116 A261692 A131328
Adjacent sequences: A103647 A103648 A103649 * A103651 A103652 A103653


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Mar 26 2005


EXTENSIONS

More terms from Robert G. Wilson v, Mar 29 2005


STATUS

approved



