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A307606 G.f. A(x) satisfies: A(x) = ((1 + x)/(1 - x)) * A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ... 2
1, 2, 6, 16, 46, 104, 268, 596, 1406, 3060, 6812, 14356, 30948, 63660, 132328, 267164, 541678, 1072000, 2127052, 4140340, 8060588, 15458948, 29602504, 55990780, 105693252, 197422424, 367793952, 679206200, 1250557768, 2284986580, 4162202864, 7530956532, 13583095710 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A307604 and A307605.

LINKS

Table of n, a(n) for n=0..32.

FORMULA

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

EXAMPLE

G.f.: A(x) = 1 + 2*x + 6*x^2 + 16*x^3 + 46*x^4 + 104*x^5 + 268*x^6 + 596*x^7 + 1406*x^8 + 3060*x^9 + ...

MATHEMATICA

terms = 32; A[_] = 1; Do[A[x_] = (1 + 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, A307604, A307605, A318767.

Sequence in context: A166896 A148440 A148441 * A098617 A291036 A092687

Adjacent sequences:  A307603 A307604 A307605 * A307607 A307608 A307609

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 18 2019

STATUS

approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)