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A229026 Expansion of 1/((1-x)*((1-5x)^2)*(1-8x)). 1
1, 19, 238, 2490, 23631, 211509, 1823908, 15348100, 127057261, 1040261799, 8453319978, 68343722910, 550640774491, 4426107030889, 35521389816448, 284771933350920, 2281370275767321, 18267889925254779, 146232526369201318, 1170331087647336130, 9365122293936867751 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence was chosen to illustrate a method of solution.

LINKS

Table of n, a(n) for n=1..21.

FORMULA

a(n) = (2*8^(n+4) - (84*n+287)*5^(n+2) - 9)/1008.

In general, for the expansion of 1/((1-t)*((1-s)^2)*(1-r)) with r > s > t, we have the formula: a(n) = (K*r^(n+3) + L*s^(n+3) + M*s^(n+2) + N*t^(n+3))/D, where K, L, M, N, D  have the following values:

K = (s-t)^2;

L = (r-t)*(r-2*s+t);

M = -(r-s)*(r-t)*(s-t)*(n+3);

N = -(r-s)^2;

D = (r-t)*((s-t)^2)*((r-s)^2).

Directly using formula we get: a(n) = (16*8^(n+3) - 7*5^(n+3) -84*(n+3)*5^n+2) - 9)/1008.  After transformation we obtain previous formula.

CROSSREFS

Sequence in context: A171158 A022033 A025938 * A114757 A142615 A021814

Adjacent sequences:  A229023 A229024 A229025 * A229027 A229028 A229029

KEYWORD

nonn

AUTHOR

Yahia Kahloune, Sep 18 2013

STATUS

approved

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Last modified September 29 17:02 EDT 2020. Contains 337432 sequences. (Running on oeis4.)