OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: -1 + (1+x)*Product_{j>=1} (1 + prime(j)*x^j).
EXAMPLE
(1+x)*(1+2*x)*(1+3*x^2)*(1+5*x^3)*(1+7*x^4)*(1+11*x^5) ... = 1 + 3*x + 5*x^2 + 14*x^3 + 28*x^4 + 57*x^5 + 126*x^6 + 239*x^7 + 436*x^8 + 830*x^9 + 1616*x^10 + ..., so the sequence begins 3, 5, 14, ...
MATHEMATICA
With[{m=51}, Rest@CoefficientList[Series[(1+x)*Product[(1+Prime[j]*x^j), {j, m+2}], {x, 0, m}], x]] (* G. C. Greubel, Oct 28 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 51); Coefficients(R!( (1+x)*(&*[1+NthPrime(j)*x^j: j in [1..52]])-1 )); // G. C. Greubel, Oct 28 2022
(SageMath)
def A147544_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( (1+x)*product(1+nth_prime(j)*x^j for j in range(1, 53)) ).list()
a=A147544_list(51); a[1:] # G. C. Greubel, Oct 28 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Neil Fernandez, Nov 06 2008
EXTENSIONS
Terms a(11) onward corrected by G. C. Greubel, Oct 28 2022
STATUS
approved