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A167432 Riordan array (c(2x)^2,xc(2x)), c(x) the g.f. of A000108. 2
1, 4, 1, 20, 6, 1, 112, 36, 8, 1, 672, 224, 56, 10, 1, 4224, 1440, 384, 80, 12, 1, 27456, 9504, 2640, 600, 108, 14, 1, 183040, 64064, 18304, 4400, 880, 140, 16, 1, 1244672, 439296, 128128, 32032, 6864, 1232, 176, 18, 1, 8599552, 3055104, 905216, 232960 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Inverse of (1-4x+4x^2,x(1-2x)) (A167431). Row sums are A084076. First column is A003645.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

Number triangle T(n,k)=A054445(n,k)*2^(n-k).

EXAMPLE

Triangle begins

1,

4, 1,

20, 6, 1,

112, 36, 8, 1,

672, 224, 56, 10, 1,

4224, 1440, 384, 80, 12, 1,

27456, 9504, 2640, 600, 108, 14, 1,

183040, 64064, 18304, 4400, 880, 140, 16, 1,

1244672, 439296, 128128, 32032, 6864, 1232, 176, 18, 1,

8599552, 3055104, 905216, 232960, 52416, 10192, 1664, 216, 20, 1,

60196864, 21498880, 6449664, 1697280, 396032, 81536, 14560, 2184, 260, 22, 1

The production matrix is

4, 1,

4, 2, 1,

8, 4, 2, 1,

16, 8, 4, 2, 1,

32, 16, 8, 4, 2, 1,

64, 32, 16, 8, 4, 2, 1,

128, 64, 32, 16, 8, 4, 2, 1,

256, 128, 64, 32, 16, 8, 4, 2, 1,

512, 256, 128, 64, 32, 16, 8, 4, 2, 1

When topped with the row (1,0,0,0...), this has inverse

1,

-4, 1,

4, -2, 1,

0, 0, -2, 1,

0, 0, 0, -2, 1,

0, 0, 0, 0, -2, 1,

0, 0, 0, 0, 0, -2, 1,

0, 0, 0, 0, 0, 0, -2, 1,

0, 0, 0, 0, 0, 0, 0, -2, 1,

0, 0, 0, 0, 0, 0, 0, 0, -2, 1

CROSSREFS

Sequence in context: A144886 A117380 A185420 * A201639 A078939 A135891

Adjacent sequences:  A167429 A167430 A167431 * A167433 A167434 A167435

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 03 2009

STATUS

approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)