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 A036970 Triangle of coefficients of Gandhi polynomials. 16
 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; text; internal format)
 OFFSET 1,3 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. - Philippe Deléham, Jun 07 2004 LINKS Robert Israel, Table of n, a(n) for n = 1..10011  (rows 1 to 141, flattened) Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014. R. B. Brent, Generalizing Tuenter's Binomial Sums, J. Int. Seq. 18 (2015) # 15.3.2. W. D. Cairns, Certain properties of binomial coefficients, Bull. Amer. Math. Soc. 26 (1920), 160-164. See p. 163 for a signed version. Dominique Dumont, Sur une conjecture de Gandhi concernant les nombres de Genocchi, Discrete Mathematics 1 (1972) 321-327. Dominique Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318. D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy) 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. Arthur Randrianarivony and Jiang Zeng, Une famille de polynomes qui interpole plusieurs suites classiques de nombres, Adv. Appl. Math. 17 (1996), 1-26. Hans J. H. Tuenter, Walking into an absolute sum, arXiv:math/0606080 [math.NT], 2006. 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 From Gary W. Adamson, Jul 19 2011: (Start) 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, ...   ... (End) Let G(n,x) = (-1)^(n+1)*B(-x,n). Then G(n,x) = (2*x/(x+1))*( 1 + 2^(2*n+1)*(x-1)/(x+2) + 3^(2*n+1)*(x-1)*(x-2)/((x+2)*(x+3)) + ... ). Cf. A083061. - Peter Bala, Feb 04 2019 EXAMPLE Triangle begins:     1;     1,   2;     3,   8,   6;    17,  54,  60,  24;   155, 556, 762, 480, 120;   ... MAPLE B[1]:= X -> X^2: for n from 2 to 12 do B[n]:= unapply(expand(X^2*(B[n-1](X+1)-B[n-1](X))), X) od: seq(seq(coeff(B[i](X), X, 1+j), j=1..i), i=1..12); # Robert Israel, Apr 21 2016 MATHEMATICA B[1][X_] = X^2; B[n_][X_] := B[n][X] = X^2*(B[n-1][X+1] - B[n-1][X]) // Simplify; Table[Coefficient[B[i][X], X, j+1], {i, 1, 12}, {j, 1, i}] // Flatten (* Jean-François Alcover, Sep 19 2018, from Maple *) CROSSREFS First 2 columns are Genocchi numbers A001469, A005440, row sums are also A001469. Cf. A083061, A272378, A272379, A272380. Sequence in context: A120390 A109230 A262992 * A110144 A327353 A270230 Adjacent sequences:  A036967 A036968 A036969 * A036971 A036972 A036973 KEYWORD tabl,nonn,easy AUTHOR EXTENSIONS More terms from David W. Wilson, Jan 12 2001 STATUS approved

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Last modified September 20 10:04 EDT 2020. Contains 337264 sequences. (Running on oeis4.)