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A253669 Square array read by ascending antidiagonals, T(n, k) = k!*[x^k](log(x+1)*sum(j=0..n, C(2*n,j)*x^j)), n>=0, k>=0. 0
0, 0, 1, 0, 1, -1, 0, 1, 3, 2, 0, 1, 7, -4, -6, 0, 1, 11, 26, 10, 24, 0, 1, 15, 74, -46, -36, -120, 0, 1, 19, 146, 342, 144, 168, 720, 0, 1, 23, 242, 1066, -756, -624, -960, -5040, 0, 1, 27, 362, 2414, 5944, 2844, 3408, 6480, 40320, 0, 1, 31, 506, 4578, 19524 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..60.

FORMULA

T(n,n) = A098118(n).

EXAMPLE

Square array starts:

[n\k][0   1   2    3     4      5       6]

[0]   0,  1, -1,   2,   -6,    24,   -120, ...

[1]   0,  1,  3,  -4,   10,   -36,    168, ...

[2]   0,  1,  7,  26,  -46,   144,   -624, ...

[3]   0,  1, 11,  74,  342,  -756,   2844, ...

[4]   0,  1, 15, 146, 1066,  5944, -15768, ...

[5]   0,  1, 19, 242, 2414, 19524, 127860, ...

[6]   0,  1, 23, 362, 4578, 48504, 434568, ...

The first few rows as a triangle:

0,

0, 1,

0, 1, -1,

0, 1,  3,   2,

0, 1,  7,  -4,  -6,

0, 1, 11,  26,  10,  24,

0, 1, 15,  74, -46, -36, -120,

0, 1, 19, 146, 342, 144,  168, 720.

MAPLE

T := (n, k) -> k!*coeff(series(ln(x+1)*add(binomial(2*n, j)*x^j, j=0..n), x, k+1), x, k): for n from 0 to 6 do lprint(seq(T(n, k), k=0..6)) od;

CROSSREFS

Cf. A098118.

Sequence in context: A081576 A292717 A054654 * A154477 A322324 A142071

Adjacent sequences:  A253666 A253667 A253668 * A253670 A253671 A253672

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Jan 18 2015

STATUS

approved

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)