A321345 -id:A321345 - cp's OEIS frontend

A321344 Expansion of 1/(1 - x) * Product_{k>=0} 1/(1 - x^(3^k))^(3^(k+1)).

1, 4, 10, 29, 71, 146, 309, 615, 1119, 2068, 3709, 6289, 10793, 18206, 29513, 48201, 77757, 121668, 191257, 297847, 452761, 690524, 1045661, 1552697, 2310786, 3419082, 4976739, 7254407, 10522736, 15052376, 21552205, 30731101, 43297942, 61039239, 85741503, 119191245

Offset: 0

Seiichi Manyama, Nov 06 2018

nonn

Also the coefficient of x^(3*n) in the expansion of Product_{k>=0} 1/(1 - x^(3^k))^(3^k).

			Product_{k>=0} 1/(1 - x^(3^k))^(3^k) = 1 + x + x^2 + 4*x^3 + 4*x^4 + 4*x^5 + 10*x^6 + 10*x^7 + 10*x^8 + 29*x^9 + 29*x^10 + 29*x^11 + ... .

Cf. A321335, A321345.

seq(n)={Vec(1/((1 - x)*prod(k=0, logint(n,3), (1 - x^(3^k) + O(x*x^n))^(3^(k+1)))))} \\ Andrew Howroyd, Nov 06 2018

A321355 Expansion of Product_{k>=0} (1 + x^(4^k))^(4^(k+1)).

Original entry on oeis.org

1, 4, 6, 4, 17, 64, 96, 64, 136, 480, 720, 480, 680, 2240, 3360, 2240, 2444, 7536, 11304, 7536, 7276, 21568, 32352, 21568, 21080, 62752, 94128, 62752, 62968, 189120, 283680, 189120, 178646, 525464, 788196, 525464, 454614, 1292992, 1939488, 1292992, 1085688, 3049760

Offset: 0

Seiichi Manyama, Nov 07 2018

nonn

Also the coefficient of x^(4*n) in the expansion of Product_{k>=0} (1 + x^(4^k))^(4^k).

			Product_{k>=0} (1 + x^(4^k))^(4^k) = 1 + x + 4*x^4 + 4*x^5 + 6*x^8 + 6*x^9 + 4*x^12 + 4*x^13 + 17*x^16 + 17*x^17 + 64*x^20 + 64*x^21 + 96*x^24 + 96*x^25 + ... .

Cf. A073708, A321345, A321354, A321357.

cp's OEIS Frontend

A321344 Expansion of 1/(1 - x) * Product_{k>=0} 1/(1 - x^(3^k))^(3^(k+1)).

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