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A115361
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Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation).
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23
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1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are the 'ruler function' A001511. Columns are stretched Fredholm-Rueppel sequences. Inverse is A115359.
Eigensequence of triangle A115361 = A018819 starting with offset 1: (1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 21 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 27 2009: (Start)
A115361 * [1, 2, 3,...] = A129527 = (1, 3, 3, 7, 5, 9, 7, 15,...).
(A115361)^(-1) * [1, 2, 3,...] = A115359 * [1, 2, 3,...] = A026741 starting /Q (1, 1, 3, 2, 5, 3, 7, 4, 9,...). (End)
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FORMULA
| Number triangle whose k-th column has g.f. x^k*sum{j>=0, (x^(2j-1))^(k+1)}.
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EXAMPLE
| Triangle begins
1;
1,1;
0,0,1;
1,1,0,1;
0,0,0,0,1;
0,0,1,0,0,1;
0,0,0,0,0,0,1;
1,1,0,1,0,0,0,1;
0,0,0,0,0,0,0,0,1;
0,0,0,0,1,0,0,0,0,1;
0,0,0,0,0,0,0,0,0,0,1;
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CROSSREFS
| Cf. A018819 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 21 2009]
Cf. A129527, A016741 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 27 2009]
Sequence in context: A014024 A014039 A016410 * A115358 A117904 A071003
Adjacent sequences: A115358 A115359 A115360 * A115362 A115363 A115364
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 21 2006
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