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
-
nmax = 15; Table[SeriesCoefficient[Product[1/(1-2^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
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{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
A292416
a(n) = [x^n] Product_{k>=1} (1 + 2^n*x^k) / (1 - 2^n*x^k).
Original entry on oeis.org
1, 4, 40, 1296, 149024, 71573568, 141871849600, 1143771307901184, 37183988027710374400, 4854666820584582571623424, 2540262650941956832151944038400, 5322109355556594174041950822678401024, 44623279107562668799968801377926722975965184
Offset: 0
-
nmax = 15; Table[SeriesCoefficient[Product[(1+2^n*x^k)/(1-2^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
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{a(n)= polcoef(prod(k=1, n, ((1+2^n*x^k)/(1-2^n*x^k) +x*O(x^n))), n)};
for(n=0,20, print1(a(n), ", ")) \\ G. C. Greubel, Feb 02 2019
A318246
a(n) = [x^n] Product_{k>=1} (1 + 3^n*x^k).
Original entry on oeis.org
1, 3, 9, 756, 6642, 118341, 388484100, 10474704297, 564988219686, 22878342156600, 12158489037532504050, 984798697643349485688, 159533936817604246934415, 19383278088136495245171156, 2616739259326831261950662430, 608267042060342812170824926328855679
Offset: 0
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nmax = 20; Table[SeriesCoefficient[Product[(1+3^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
A318247
a(n) = [x^n] Product_{k>=1} (1 + n!*x^k).
Original entry on oeis.org
1, 1, 2, 42, 600, 28920, 374285520, 128100273840, 131101518683520, 143354704247556480, 173401404266683545849388800, 2538767479410416957720411116800, 105287752487031026606448840363801600, 4510685217145833106538730603088118860800, 288804138719404983322786510403231912442931200
Offset: 0
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nmax = 15; Table[SeriesCoefficient[Product[(1+n!*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
Showing 1-4 of 4 results.
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