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A290000 a(n) = Product_{k=1..n-1} (3^k + 1). 1
1, 1, 4, 40, 1120, 91840, 22408960, 16358540800, 35792487270400, 234870301468364800, 4623187014103292723200, 272999193182799435304960000, 48361261073946554365403054080000, 25701205307660304745058529866383360000, 40976048450930207702360695570691784048640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

FORMULA

G.f. A(x) satisfies: A(x) = 1 + x * A(3*x) / (1 - x).

G.f.: Sum_{k>=0} 3^(k*(k - 1)/2) * x^k / Product_{j=0..k-1} (1 - 3^j*x).

a(0) = 1; a(n) = Sum_{k=0..n-1} 3^k * a(k).

a(n) ~ c * 3^(n*(n - 1)/2), where c = Product_{k>=1} (1 + 1/3^k) = 1.564934018567011537938849... = A132324.

MATHEMATICA

Table[Product[3^k + 1, {k, 1, n - 1}], {n, 0, 14}]

PROG

(PARI) a(n) = prod(k=1, n-1, 3^k + 1); \\ Michel Marcus, Jun 06 2020

CROSSREFS

Cf. A027871, A028362, A034472, A047656, A132324, A309327, A323716.

Sequence in context: A013108 A173945 A111846 * A102922 A139688 A197356

Adjacent sequences:  A289997 A289998 A289999 * A290001 A290002 A290003

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 06 2020

STATUS

approved

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)