OFFSET
0,10
COMMENTS
Invert transform of A010815.
Alternating row sums of Riordan triangle (1, 1 - Product_{j>=1} (1-x^j) ), See A341418(n, m) without column {1, repeat(0)} for m = 0 and n >= 0. - Wolfdieter Lang, Feb 17 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A010815(k)*a(n-k).
G.f.: 1/(2 - QPochhammer(x)). - G. C. Greubel, Sep 08 2023
MATHEMATICA
nmax=65; CoefficientList[Series[1/(2 - Product[(1 - x^k), {k, nmax}]), {x, 0, nmax}], x]
PROG
(Magma)
m:=80;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( 1/(2 - (&*[1 - x^j: j in [1..m+2]])) )); // G. C. Greubel, Sep 08 2023
(SageMath)
from sage.modular.etaproducts import qexp_eta
m=80;
def f(x): return 1/(2 - qexp_eta(QQ[['q']], m+2).subs(q=x) )
def A307059_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).list()
A307059_list(m) # G. C. Greubel, Sep 08 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Mar 21 2019
STATUS
approved