A292416 -id:A292416 - cp's OEIS frontend

A292414 a(n) = [x^n] Product_{k>=1} (1 + 2^n*x^k).

1, 2, 4, 72, 272, 2080, 270400, 2146432, 33751296, 403702272, 1103810790400, 17635156690944, 563431073648640, 13515197331283968, 360331952265379840, 37785849814204784082944, 1209091844251972299456512, 77374499118322174520328192, 3713890953695657990811811840

Offset: 0

Vaclav Kotesovec, Sep 16 2017

Vaclav Kotesovec, Table of n, a(n) for n = 0..183

Cf. A292304, A292415, A292416.

nmax = 20; Table[SeriesCoefficient[Product[(1+2^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

{a(n)= polcoef(prod(k=1, n, (1+2^n*x^k +x*O(x^n))), n)};
for(n=0,20, print1(a(n), ", ")) \\ G. C. Greubel, Feb 02 2019

Conjecture: log(a(n)) ~ sqrt(2)*log(2)*n^(3/2). - Vaclav Kotesovec, Aug 22 2018

A292415 a(n) = [x^n] Product_{k>=1} (1 / (1 - 2^n*x^k)).

Original entry on oeis.org

1, 2, 20, 584, 70160, 34670624, 69827571776, 567417533153408, 18519367937794769152, 2422592506675732350501376, 1268890961666701371908767613952, 2659755334364276805914758224778627072, 22306192375831301664022382396371369078034432

Offset: 0

Vaclav Kotesovec, Sep 16 2017

nonn

G. C. Greubel, Table of n, a(n) for n = 0..57

Cf. A292414, A292416.

nmax = 15; Table[SeriesCoefficient[Product[1/(1-2^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

{a(n)= polcoef(prod(k=1, n, 1/(1-2^n*x^k +x*O(x^n))), n)};
for(n=0,20, print1(a(n), ", ")) \\ G. C. Greubel, Feb 02 2019

a(n) ~ 2^(n^2).

cp's OEIS Frontend

A292414 a(n) = [x^n] Product_{k>=1} (1 + 2^n*x^k).

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