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A305031 Expansion of ((1 + 2*x)/(1 - 2*x))^(3/2). 3
1, 6, 18, 44, 102, 228, 500, 1080, 2310, 4900, 10332, 21672, 45276, 94248, 195624, 404976, 836550, 1724580, 3549260, 7293000, 14965236, 30669496, 62783448, 128388624, 262303132, 535422888, 1092063000, 2225728400, 4533175800, 9226818000, 18769219920, 38158909920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let ((1 + k*x)/(1 - k*x))^(m/k) = a(0) + a(1)*x + a(2)*x^2 + ...

Then n*a(n) = 2*m*a(n-1) + k^2*(n-2)*a(n-2) for n > 1.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..3000

FORMULA

n*a(n) = 6*a(n-1) + 4*(n-2)*a(n-2) for n > 1.

a(n) ~ 2^(n + 5/2) * sqrt(n/Pi). - Vaclav Kotesovec, May 28 2018

PROG

(PARI) N=66; x='x+O('x^N); Vec(((1+2*x)/(1-2*x))^(3/2))

CROSSREFS

((1 + 2*x)/(1 - 2*x))^(m/2): A063886 (m=1), this sequence (m=3), A241204 (m=4).

Cf. A304941, A305032.

Sequence in context: A303649 A095170 A261647 * A031128 A304161 A261016

Adjacent sequences:  A305028 A305029 A305030 * A305032 A305033 A305034

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 24 2018

STATUS

approved

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Last modified May 12 11:55 EDT 2021. Contains 343821 sequences. (Running on oeis4.)