A163318 Expansion of g.f.: Product_{k>=1} 1+k*x^k/(1-x^k)^2.

1, 1, 4, 8, 19, 36, 76, 142, 272, 496, 900, 1592, 2784, 4792, 8138, 13688, 22703, 37380, 60838, 98310, 157298, 250162, 394332, 618032, 961512, 1487563, 2286610, 3496776, 5316666, 8044598, 12110538, 18147166, 27068692, 40203306, 59459998, 87587428, 128522850

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1) +add(b(n-i*j, i-1)*(j*i), j=1..n/i)))
    end:
a:= n-> b(n, n):
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 25 2013

Mathematica

terms = 40;
CoefficientList[Product[1 + k x^k/(1 - x^k)^2, {k, 1, terms}] + O[x]^terms, x] (* Jean-François Alcover, Nov 12 2020 *)

Crossrefs

Cf. A006906, A077285, A162506.

Sequence in context: A130887 A049933 A301746 * A129362 A301981 A083579

Adjacent sequences: A163315 A163316 A163317 * A163319 A163320 A163321

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 24 2009

Status

approved