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A108085 Triangle, read by rows, where T(0,0) = 1, T(n,k) = 2^n*T(n-1,k) - T(n-1,k-1). 0
1, 2, -1, 8, -6, 1, 64, -56, 14, -1, 1024, -960, 280, -30, 1, 32768, -31744, 9920, -1240, 62, -1, 2097152, -2064384, 666624, -89280, 5208, -126, 1, 268435456, -266338304, 87392256, -12094464, 755904, -21336, 254, -1, 68719476736, -68451041280, 22638755840, -3183575040, 205605888, -6217920 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n > 0, n-th row sum = Product_{i=1..n} (2^i - 1), i.e., A005329(n).

Triangle T(n,k), 0 <= k <= n, read by rows given by [2, 2, 8, 12, 32, 56, 128, 240, 512, ...] DELTA [[ -1, 0, -2, 0, -4, 0, -8, 0, -16, 0, -32, 0, ...] = A014236(first zero omitted)DELTA -A077957 where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 23 2006

LINKS

Table of n, a(n) for n=0..41.

EXAMPLE

Triangle begins

     1;

     2,   -1;

     8,   -6,   1;

    64,  -56,  14,  -1;

  1024, -960, 280, -30, 1;

PROG

(PARI) t(n, k) = {if (k < 0, return (0)); if (n < k, return (0)); if (n == 0, return (1)); return (2^n*t(n-1, k) - t(n-1, k-1)); }  \\ Michel Marcus, Apr 11 2013

CROSSREFS

Sequence in context: A039683 A318389 A108084 * A305860 A272983 A195698

Adjacent sequences:  A108082 A108083 A108084 * A108086 A108087 A108088

KEYWORD

sign,tabl

AUTHOR

Gerald McGarvey, Jun 05 2005

STATUS

approved

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Last modified June 4 05:19 EDT 2020. Contains 334815 sequences. (Running on oeis4.)