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A307605 G.f. A(x) satisfies: A(x) = (1 + x) * A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ... 3
1, 1, 2, 5, 12, 20, 48, 81, 169, 305, 580, 1009, 1966, 3338, 6067, 10503, 18730, 31633, 55641, 93151, 160389, 267585, 452762, 747016, 1253644, 2049943, 3390786, 5516227, 9034745, 14572790, 23668066, 37918484, 61042425, 97231826, 155292944, 245774727, 389998116 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Weigh transform of A050369.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^(k*A074206(k)).

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 20*x^5 + 48*x^6 + 81*x^7 + 169*x^8 + 305*x^9 + ...

MATHEMATICA

terms = 36; A[_] = 1; Do[A[x_] = (1 + x) Product[A[x^k]^k, {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

CROSSREFS

Cf. A050369, A074206, A129373, A307604, A307606.

Sequence in context: A095306 A258602 A327065 * A079648 A080838 A244396

Adjacent sequences:  A307602 A307603 A307604 * A307606 A307607 A307608

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 18 2019

STATUS

approved

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Last modified April 6 22:23 EDT 2020. Contains 333291 sequences. (Running on oeis4.)