A321335 -id:A321335 - 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

A321345 Expansion of 1/(1 - x) * Product_{k>=0} 1/(1 - x^(4^k))^(4^(k+1)).

Original entry on oeis.org

1, 5, 15, 35, 86, 206, 450, 890, 1751, 3411, 6401, 11405, 20076, 35036, 59876, 99156, 162345, 263821, 422871, 663691, 1031914, 1594610, 2440286, 3678886, 5504759, 8196659, 12117745, 17715581, 25744904, 37267624, 53652824, 76576760, 108763319, 153984019, 217058009

Offset: 0

Seiichi Manyama, Nov 06 2018

nonn

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

			Product_{k>=0} 1/(1 - x^(4^k))^(4^k) = 1 + x + x^2 + x^3 + 5*x^4 + 5*x^5 + 5*x^6 + 5*x^7 + 15*x^8 + 15*x^9 + 15*x^10 + 15*x^11 + 35*x^12 + 35*x^13 + 35*x^14 + 35*x^15 + ... .

Cf. A321335, A321344.

seq(n)={Vec(1/((1 - x)*prod(k=0, logint(n,4), (1 - x^(4^k) + O(x*x^n))^(4^(k+1)))))} \\ Andrew Howroyd, Nov 06 2018

A321336 Expansion of Product_{k>=0} (1 - x^(2^k))^(2^(k+1)).

Original entry on oeis.org

1, -2, -3, 8, -6, 4, 26, -56, -7, 70, -51, 32, 120, -272, -200, 672, -182, -308, 1026, -1744, -660, 3064, -916, -1232, 2466, -3700, -3990, 11680, -1416, -8848, 13752, -18656, -8503, 35662, -14331, -7000, 27122, -47244, -29870, 106984, -25895, -55194, 140173, -225152

Offset: 0

Seiichi Manyama, Nov 05 2018

sign

Cf. A073708, A321327, A321335.

Equals the self-convolution of A321327.
G.f.: A(x) satisfies A(x) = ((1 - x) * A(x^2))^2, with A(0) = 1.
a(n) = A321327(2*n) for n >= 0.

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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A321345 Expansion of 1/(1 - x) * Product_{k>=0} 1/(1 - x^(4^k))^(4^(k+1)).

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A321336 Expansion of Product_{k>=0} (1 - x^(2^k))^(2^(k+1)).

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