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

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

0,2

Comments

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

Links

Table of n, a(n) for n=0..34.

Example

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 + ... .

Prog

(PARI) 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

Crossrefs

Cf. A321335, A321344.

Sequence in context: A322048 A143695 A019531 * A145454 A292912 A346755

Adjacent sequences: A321342 A321343 A321344 * A321346 A321347 A321348

Keyword

nonn

Author

Seiichi Manyama, Nov 06 2018

Status

approved