login
A022728
Expansion of Product_{m>=1} (1-m*q^m)^-4.
2
1, 4, 18, 64, 219, 676, 2030, 5736, 15793, 41864, 108430, 273240, 675526, 1634780, 3891960, 9108872, 21018870, 47815572, 107446898, 238524144, 523812125, 1138233100, 2449710880, 5223395480, 11042278208
OFFSET
0,2
COMMENTS
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 4, g(n) = n. - Seiichi Manyama, Dec 29 2017
LINKS
FORMULA
G.f.: exp(4*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-4, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)
PROG
(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^-4)) \\ G. C. Greubel, Jul 25 2018
(Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^4:m in [1..n]])); // G. C. Greubel, Jul 25 2018
CROSSREFS
Column k=4 of A297328.
Sequence in context: A083321 A362316 A255611 * A231950 A246134 A115112
KEYWORD
nonn
STATUS
approved