|
| |
|
|
A301271
|
|
Expansion of (1-16*x)^(1/8).
|
|
4
|
|
|
|
1, -2, -14, -140, -1610, -19964, -259532, -3485144, -47920730, -670890220, -9526641124, -136837208872, -1984139528644, -28998962341720, -426699017313880, -6315145456245424, -93937788661650682, -1403541077650545484, -21053116164758182260, -316904801216886322440
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 0..833
|
|
|
FORMULA
|
a(n) = 2^n/n! * Product_{k=0..n-1} (8*k - 1) for n > 0.
a(n) = -sqrt(2-sqrt(2)) * Gamma(1/8) * Gamma(n-1/8) * 16^(n-1) / (Pi*Gamma(n+1)). - Vaclav Kotesovec, Jun 16 2018
a(n) ~ -2^(4*n-3) / (Gamma(7/8) * n^(9/8)). - Vaclav Kotesovec, Jun 16 2018
D-finite with recurrence: n*a(n) +2*(-8*n+9)*a(n-1)=0. - R. J. Mathar, Jan 20 2020
a(n) = -2*A097184(n-1). - R. J. Mathar, Jan 20 2020
|
|
|
PROG
|
(PARI) N=20; x='x+O('x^N); Vec((1-16*x)^(1/8))
|
|
|
CROSSREFS
|
Cf. A003557, A007947.
(1-b*x)^(1/A003557(b)): A002420 (b=4), A004984 (b=8), A004990 (b=9), (-1)^n * A108735 (b=12), this sequence (b=16), (-1)^n * A108733 (b=18), A049393 (b=25), A004996 (b=36), A303007 (b=240), A303055 (b=504), A305886 (b=1728).
Sequence in context: A224729 A355722 A303395 * A245267 A328004 A271564
Adjacent sequences: A301268 A301269 A301270 * A301272 A301273 A301274
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
Seiichi Manyama, Jun 15 2018
|
|
|
STATUS
|
approved
|
| |
|
|
