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A165293 Inverse of A038303, and generalization of A130595. 4
1, 10, -1, 100, -20, 1, 1000, -300, 30, -1, 10000, -4000, 600, -40, 1, 100000, -50000, 10000, -1000, 50, -1, 1000000, -600000, 150000, -20000, 1500, -60, 1, 10000000, -7000000, 2100000, -350000, 35000, -2100, 70 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Rows sum up to A001019 (powers of 9), diagonals to A004189, a generalization of A010892 (the inverse Fibonacci). Ratio of diagonal sums converges to a decimal sequence: A000108 (Catalan numbers), which is the squared difference of sqrt(2) and sqrt(3), or 5-sqrt(24). Ratio between first binomial transform (A054320 and A138288)of A004189, converges to sqrt(2/3). 1/(2*sqrt(24)) gives A000984 (central binomial coefficients) as a decimal sequence.

Triangle T(n,k), read by rows, given by [10,0,0,0,0,0,0,0,...] DELTA [ -1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 15 2009

LINKS

Table of n, a(n) for n=1..35.

FORMULA

Sum_{k=0..n} T(n,k)*x^k = (10-x)^n. - Philippe Deléham, Dec 15 2009

G.f.: x*y/(1-10*x+x*y). - R. J. Mathar, Aug 11 2015

EXAMPLE

Triangle begins:

      1;

     10,    -1;

    100,   -20,   1;

   1000,  -300,  30,  -1;

  10000, -4000, 600, -40, 1;

CROSSREFS

Cf. A007318, A130595, A038303, A004189, A010892, A001079, A054320, A138288, A041041, A000108.

Sequence in context: A178865 A164881 A276379 * A038303 A178870 A075505

Adjacent sequences:  A165290 A165291 A165292 * A165294 A165295 A165296

KEYWORD

tabl,sign

AUTHOR

Mark Dols, Sep 13 2009

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)