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A307399 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} k*x^k*A(x)^k/(1 - x^k*A(x)^k). 3
1, 1, 4, 14, 60, 262, 1218, 5798, 28364, 141239, 714532, 3660098, 18949830, 98997082, 521218206, 2762807736, 14731968812, 78968221213, 425282844540, 2299997984844, 12485972925500, 68015653648096, 371666798915578, 2036765196573550, 11190993772943502, 61637787236407747 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} sigma(k)*x^k*A(x)^k.

G.f.: A(x) = (1/x)*Series_Reversion(x/(1 + Sum_{k>=1} sigma(k)*x^k)).

a(n) ~ c * d^n / n^(3/2), where d = 5.84278321476352032847350429253643509033417800773284061845774243558820314... and c = 0.5552806478004840811027181339325620905324642078294... - Vaclav Kotesovec, Apr 07 2019

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 14*x^3 + 60*x^4 + 262*x^5 + 1218*x^6 + 5798*x^7 + 28364*x^8 + 141239*x^9 + 714532*x^10 + ...

MATHEMATICA

terms = 26; A[_] = 0; Do[A[x_] = 1 + Sum[k x^k A[x]^k/(1 - x^k A[x]^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

terms = 26; A[_] = 0; Do[A[x_] = 1 + Sum[DivisorSigma[1, k] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

terms = 26; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[DivisorSigma[1, k]  x^k, {k, 1, terms}]), {x, 0, terms}], x], x]

CROSSREFS

Cf. A000203, A192206, A307397, A307401.

Sequence in context: A111276 A149493 A299926 * A307411 A259104 A082033

Adjacent sequences:  A307396 A307397 A307398 * A307400 A307401 A307402

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 07 2019

STATUS

approved

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Last modified February 25 18:40 EST 2020. Contains 332256 sequences. (Running on oeis4.)