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A247505 Generalized Lucas numbers: square array A(n,k) read by antidiagonals, A(n,k)=(-1)^(k+1)*k*[x^k](-log((1+sum_{j=1..n}(-1)^(j+1)*x^j))^(-1))), (n>=0, k>=0). 3
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 3, 1, 0, 0, 1, 3, 4, 1, 0, 0, 1, 3, 7, 7, 1, 0, 0, 1, 3, 7, 11, 11, 1, 0, 0, 1, 3, 7, 15, 21, 18, 1, 0, 0, 1, 3, 7, 15, 26, 39, 29, 1, 0, 0, 1, 3, 7, 15, 31, 51, 71, 47, 1, 0, 0, 1, 3, 7, 15, 31, 57, 99, 131, 76, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Table of n, a(n) for n=0..77.

EXAMPLE

n\k[0][1][2][3] [4] [5] [6]  [7]  [8]  [9]  [10]  [11]  [12]

[0] 0, 0, 0, 0,  0,  0,  0,   0,   0,   0,    0,    0,    0

[1] 0, 1, 1, 1,  1,  1,  1,   1,   1,   1,    1,    1,    1

[2] 0, 1, 3, 4,  7, 11, 18,  29,  47,  76,  123,  199,  322 [A000032]

[3] 0, 1, 3, 7, 11, 21, 39,  71, 131, 241,  443,  815, 1499 [A001644]

[4] 0, 1, 3, 7, 15, 26, 51,  99, 191, 367,  708, 1365, 2631 [A073817]

[5] 0, 1, 3, 7, 15, 31, 57, 113, 223, 439,  863, 1695, 3333 [A074048]

[6] 0, 1, 3, 7, 15, 31, 63, 120, 239, 475,  943, 1871, 3711 [A074584]

[7] 0, 1, 3, 7, 15, 31, 63, 127, 247, 493,  983, 1959, 3903 [A104621]

[8] 0, 1, 3, 7, 15, 31, 63, 127, 255, 502, 1003, 2003, 3999 [A105754]

[.] .  .  .  .   .   .   .    .    .    .     .     .     .

oo] 0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095 [A000225]

'

As a triangular array, starts:

0,

0, 0,

0, 1, 0,

0, 1, 1, 0,

0, 1, 3, 1, 0,

0, 1, 3, 4, 1, 0,

0, 1, 3, 7, 7, 1,  0,

0, 1, 3, 7, 11, 11, 1, 0,

0, 1, 3, 7, 15, 21, 18, 1, 0,

0, 1, 3, 7, 15, 26, 39, 29, 1, 0,

MAPLE

A := proc(n, k) f := -log((1+add((-1)^(j+1)*x^j, j=1..n))^(-1));

(-1)^(k+1)*k*coeff(series(f, x, k+2), x, k) end:

seq(print(seq(A(n, k), k=0..12)), n=0..8);

MATHEMATICA

A[n_, k_] := Module[{f, x}, f = -Log[(1+Sum[(-1)^(j+1) x^j, {j, 1, n}] )^(-1)]; (-1)^(k+1) k SeriesCoefficient[f, {x, 0, k}]];

Table[A[n-k, k], {n, 0, 12}, {k, 0, n}] (* Jean-Fran├žois Alcover, Jun 28 2019, from Maple *)

CROSSREFS

Cf. A247506, A000225, A000032, A001644, A073817, A074048, A074584, A104621, A105754.

Cf. A125127.

Sequence in context: A062734 A205531 A269246 * A117389 A122083 A098158

Adjacent sequences:  A247502 A247503 A247504 * A247506 A247507 A247508

KEYWORD

tabl,nonn

AUTHOR

Peter Luschny, Nov 02 2014

STATUS

approved

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Last modified August 24 14:13 EDT 2019. Contains 326283 sequences. (Running on oeis4.)