A305882 - OEIS

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A305882

-1 + Product_{n>=1} 1/(1 + a(n)*x^n) = g.f. of A000040 (prime numbers).

-2, 1, 1, 4, 4, 13, 16, 44, 52, 112, 182, 411, 620, 1318, 2142, 5148, 7676, 15228, 27530, 58660, 98372, 207392, 364464, 763263, 1341508, 2773990, 4923220, 10470948, 18510902, 37546152, 69269976, 148419094, 258284232, 534761242, 981480012, 2004302204

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

FORMULA

Product_{n>=1} 1/(1 + a(n)*x^n) = 1 + Sum_{k>=1} prime(k)*x^k.

Product_{n>=1} (1 + a(n)*x^n) = Sum_{k>=0} A030018(k)*x^k.

EXAMPLE

1/((1 - 2*x) * (1 + x^2) * (1 + x^3) * (1 + 4*x^4) * (1 + 4*x^5) * ... * (1 + a(n)*x^n) * ...) = 1 + 2*x + 3*x^2 + 5*x^3 + 7*x^4 + 11*x^5 + ... + A000040(k)*x^k + ...

CROSSREFS

Cf. A000040, A030010, A030018, A145519, A147541, A147557, A305871, A305881.

Sequence in context: A357050 A197380 A057785 * A339285 A363043 A192404

Adjacent sequences: A305879 A305880 A305881 * A305883 A305884 A305885

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 13 2018

STATUS

approved