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%I #15 Oct 29 2022 07:08:44
%S 3,5,14,28,57,126,239,436,830,1616,2806,4975,8578,14914,26825,45148,
%T 73742,124446,205326,333878,560588,903857,1431876,2275324,3633808,
%U 5713071,9019922,14309452,22104630,34018220,52450816,80023048,122423244,186079122,282089161,431595854,647808336,966099832,1442708500
%N Coefficient of x^n in product (1+x)*Product_{j>=1} (1 + prime(j)*x^j).
%H G. C. Greubel, <a href="/A147544/b147544.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: -1 + (1+x)*Product_{j>=1} (1 + prime(j)*x^j).
%e (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, ...
%t 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 *)
%o (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
%o (SageMath)
%o def A147544_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P( (1+x)*product(1+nth_prime(j)*x^j for j in range(1,53)) ).list()
%o a=A147544_list(51); a[1:] # _G. C. Greubel_, Oct 28 2022
%Y Cf. A000040, A147541.
%K nonn
%O 1,1
%A _Neil Fernandez_, Nov 06 2008
%E Terms a(11) onward corrected by _G. C. Greubel_, Oct 28 2022
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