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A291261 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of continued fraction 1/(1 - x/(1 - 3^k*x/(1 - 5^k*x/(1 - 7^k*x/(1 - 9^k*x/(1 - ...)))))). 2
1, 1, 1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 10, 31, 14, 1, 1, 28, 325, 364, 42, 1, 1, 82, 4159, 22150, 5746, 132, 1, 1, 244, 57349, 1790452, 2586250, 113944, 429, 1, 1, 730, 818911, 162045118, 1691509906, 461242900, 2719291, 1430, 1, 1, 2188, 11923525, 15520964284, 1289803048426, 2978600051368, 116651486125, 75843724, 4862 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..54.

FORMULA

G.f. of column k: 1/(1 - x/(1 - 3^k*x/(1 - 5^k*x/(1 - 7^k*x/(1 - 9^k*x/(1 - ...)))))), a continued fraction.

EXAMPLE

Square array begins:

   1,     1,        1,           1,              1,                 1,  ...

   1,     1,        1,           1,              1,                 1,  ...

   2,     4,       10,          28,             82,               244,  ...

   5,    31,      325,        4159,          57349,            818911,  ...

  14,   364,    22150,     1790452,      162045118,       15520964284,  ...

  42,  5746,  2586250,  1691509906,  1289803048426,  1063421637466546,  ...

MATHEMATICA

Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i - 1)^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 9}, {n, 0, j}] // Flatten

CROSSREFS

Columns k=0..2 give A000108, A128709, A127823.

Main diagonal gives A291332.

Cf. A034472 (row 2), A290569, A291260.

Sequence in context: A057785 A305882 A192404 * A294206 A263284 A158471

Adjacent sequences:  A291258 A291259 A291260 * A291262 A291263 A291264

KEYWORD

nonn,tabl

AUTHOR

Ilya Gutkovskiy, Aug 21 2017

STATUS

approved

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Last modified May 26 22:57 EDT 2019. Contains 323597 sequences. (Running on oeis4.)