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A271236 G.f.: Product_{k>=1} 1/(1 - (9*x)^k)^(1/3). 7
1, 3, 45, 450, 5805, 52326, 705591, 6190425, 77219325, 751178610, 8522919063, 80502824835, 975122402985, 8949951461925, 100088881882830, 1003346683458480, 10828622925516312, 104307212166072165, 1152197107898173875, 11048535008792967825, 119509353627934830327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, for h>=1, if g.f. = Product_{k>=1} 1/(1-(h^2*x)^k)^(1/h), then a(n) ~ h^(2*n) * exp(Pi*sqrt(2*n/(3*h))) / (2^(5*h+3) * 3^(h+1) * h^(h+1) * n^(3*h+1))^(1/(4*h)).

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/3, g(n) = 9^n. - Seiichi Manyama, Apr 20 2018

LINKS

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

FORMULA

a(n) ~ 3^(2*n - 2/3) * exp(sqrt(2*n)*Pi/3) / (2^(3/2) * n^(5/6)).

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[1/(1 - (9*x)^k)^(1/3), {k, 1, nmax}], {x, 0, nmax}], x]

PROG

(PARI) N=99; x='x+O('x^N); Vec(prod(k=1, N, 1/(1-(9*x)^k)^(1/3))) \\ Altug Alkan, Apr 20 2018

CROSSREFS

Cf. A298994, A303074, A303130, A303152, A303342.

Expansion of Product_{n>=1} (1 - ((b^2)*x)^n)^(-1/b): A000041 (b=1), A271235 (b=2), this sequence (b=3), A303135 (b=4), A303136 (b=5).

Sequence in context: A117972 A061532 A060242 * A270064 A141445 A076140

Adjacent sequences:  A271233 A271234 A271235 * A271237 A271238 A271239

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Apr 02 2016

STATUS

approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)