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A291260 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of continued fraction 1/(1 - 2^k*x/(1 - 4^k*x/(1 - 6^k*x/(1 - 8^k*x/(1 - 10^k*x/(1 - ...)))))). 2
1, 1, 1, 1, 2, 2, 1, 4, 12, 5, 1, 8, 80, 120, 14, 1, 16, 576, 3904, 1680, 42, 1, 32, 4352, 152064, 354560, 30240, 132, 1, 64, 33792, 6492160, 99422208, 51733504, 665280, 429, 1, 128, 266240, 290488320, 31832735744, 130292416512, 11070525440, 17297280, 1430 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..44.

FORMULA

G.f. of column k: 1/(1 - 2^k*x/(1 - 4^k*x/(1 - 6^k*x/(1 - 8^k*x/(1 - 10^k*x/(1 - ...)))))), a continued fraction.

EXAMPLE

Square array begins:

:  1,     1,        1,            1,               1, ...

:  1,     2,        4,            8,              16, ...

:  2,    12,       80,          576,            4352, ...

:  5,   120,     3904,       152064,         6492160, ...

: 14,  1680,   354560,     99422208,     31832735744, ...

: 42, 30240, 51733504, 130292416512, 390365719822336, ...

MATHEMATICA

Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i)^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 8}, {n, 0, j}] // Flatten

CROSSREFS

Columns k=0-2 give A000108, A001813, A002436.

Main diagonal gives A291331.

Cf. A000079 (row 1), A063481 (row 2), A290569, A291261.

Sequence in context: A086873 A101560 A307456 * A218529 A192456 A226948

Adjacent sequences:  A291257 A291258 A291259 * A291261 A291262 A291263

KEYWORD

nonn,tabl

AUTHOR

Ilya Gutkovskiy, Aug 21 2017

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)