OFFSET
0,3
COMMENTS
Is a(9) the only occurrence of 0 in this sequence? - Robert Israel, Jun 02 2015
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
MAPLE
P:= mul(1-m*q^m, m=1..100):
S:= series(P, q, 101):
seq(coeff(S, q, j), j=0..100); # Robert Israel, Jun 02 2015
# second Maple program:
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, b(n, i-1)-`if`(i>n, 0, i*b(n-i, i-1))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60); # Sean A. Irvine (after Alois P. Heinz), May 19 2019
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[1 - k*x^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 15 2015 *)
nmax = 40; CoefficientList[Series[Exp[-Sum[PolyLog[-j, x^j]/j, {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 15 2015 *)
(* More efficient program: *) nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = -1; Do[Do[poly[[j+1]] -= k*poly[[j-k+1]], {j, nmax, k, -1}]; , {k, 2, nmax}]; poly (* Vaclav Kotesovec, Jan 07 2016 *)
PROG
(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n))) \\ G. C. Greubel, Feb 18 2018
(Magma) Coefficients(&*[(1-m*x^m):m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 18 2018
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved