A285245 Expansion of Product_{k>=1} 1/(1 - k*x^(k^2)).

1, 1, 1, 1, 3, 3, 3, 3, 7, 10, 10, 10, 18, 24, 24, 24, 44, 56, 65, 65, 105, 129, 147, 147, 227, 292, 328, 355, 515, 645, 717, 771, 1107, 1367, 1562, 1670, 2429, 2949, 3339, 3555, 5073, 6181, 6961, 7546, 10582, 13059, 14619, 15789, 21925, 26886, 30235, 32575

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ c * 2^(n/4), where

c = 6.362854320457366874306510139107365081972383711876544726... if mod(n,4)=0

c = 6.470997903106304472752360748461108347899808941622559468... if mod(n,4)=1

c = 6.154059402265470959096395812318265046714869376472639022... if mod(n,4)=2

c = 5.624747659153211728892605407048217108787120474872434485... if mod(n,4)=3

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - k*x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001156, A006906, A285243, A285244.

Sequence in context: A369233 A092531 A125002 * A098528 A242715 A078229

Adjacent sequences: A285242 A285243 A285244 * A285246 A285247 A285248

Keyword

nonn

Author

Vaclav Kotesovec, Apr 15 2017

Status

approved