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A036970
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Triangle of coefficients of Gandhi polynomials.
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7
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1, 1, 2, 3, 8, 6, 17, 54, 60, 24, 155, 556, 762, 480, 120, 2073, 8146, 12840, 10248, 4200, 720, 38227, 161424, 282078, 263040, 139440, 40320, 5040, 929569, 4163438, 7886580, 8240952, 5170800, 1965600, 423360, 40320, 28820619, 135634292
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Another version of triangle T(n,k), 0<=k<=n, read by rows; given by [0, 1, 2, 4, 6, 9, 12, 16, 20, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, ...] = 1; 0, 1; 0, 1, 2; 0, 3, 8, 6; 0, 17, 54, 60, 24; ... where DELTA is the operator defined in A084938 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 07 2004
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REFERENCES
| D. Dumont, Sur une conjecture de Gandhi concernant les nombers de Genocchi. Discrete Mathematics 1 (1972) 321-327.
D. Dumont, Interpretations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.
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LINKS
| Marc Joye, Pascal Paillier and Berry Schoenmakers, On Second-Order Differential Power Analysis, in Cryptographic Hardware and Embedded Systems-CHES 2005, editors: Josyula R. Rao and Berk Sunar, Lecture Notes in Computer Science 3659 (2005) 293-308, Springer-Verlag.
A. Randrianarivony and J. Zeng, Une famille des polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26.
H. J. H. Tuenter, Walking into an absolute sum
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FORMULA
| Let B(X, n) = X^2 (B(X+1, n-1) - B(X, n-1)), B(X, 1) = X^2; then the (i, j)-th entry in the table is the coefficient of X^(1+j) in B(X, i). - Mike Domaratzki (mdomaratzki(AT)alumni.uwaterloo.ca), Nov 17 2001
n-th row = top row of M^(n-1), M = an infinite square matrix in which the first "1" and right border of 1's of Pascal's triangle are deleted, as follows:
1, 2, 0, 0, 0, 0, ...
1, 3, 3, 0, 0, 0, ...
1, 4, 6, 4, 0, 0, ...
1, 5, 10, 10, 5, 0, ...
1, 6, 15, 20, 15, 6, ...
...
- Gary W. Adamson, Jul 19 2011
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EXAMPLE
| Triangle begins:
1;
1,2;
3,8,6;
17,54,60,24;
155,556,762,480,120;
...
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CROSSREFS
| First 2 columns are A001469, A005440, row sums are also A001469.
Sequence in context: A112977 A120390 A109230 * A110144 A183141 A196828
Adjacent sequences: A036967 A036968 A036969 * A036971 A036972 A036973
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KEYWORD
| tabl,nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 12 2001
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