|
|
A147544
|
|
Coefficient of x^n in product (1+x)*Product_{j>=1} (1 + prime(j)*x^j).
|
|
1
|
|
|
3, 5, 14, 28, 57, 126, 239, 436, 830, 1616, 2806, 4975, 8578, 14914, 26825, 45148, 73742, 124446, 205326, 333878, 560588, 903857, 1431876, 2275324, 3633808, 5713071, 9019922, 14309452, 22104630, 34018220, 52450816, 80023048, 122423244, 186079122, 282089161, 431595854, 647808336, 966099832, 1442708500
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
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)
P.<x> = PowerSeriesRing(QQ, prec)
return P( (1+x)*product(1+nth_prime(j)*x^j for j in range(1, 53)) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|