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 A065547 Triangle of Salie numbers. 16
 1, 0, 1, 0, -1, 1, 0, 3, -3, 1, 0, -17, 17, -6, 1, 0, 155, -155, 55, -10, 1, 0, -2073, 2073, -736, 135, -15, 1, 0, 38227, -38227, 13573, -2492, 280, -21, 1, 0, -929569, 929569, -330058, 60605, -6818, 518, -28, 1, 0, 28820619, -28820619, 10233219, -1879038, 211419, -16086, 882, -36, 1, 0, -1109652905 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Coefficients of polynomials H(n,x) related to Euler polynomials through H(n,x(x-1)) = E(2n,x). LINKS D. Dumont and J. Zeng, Polynomes d'Euler et les fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998) 3, 387-410. J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23. Ira M. Gessel and X. G. Viennot, Determinants, paths and plane partitions, 1989, p. 27, eqn 12.1. A. F. Horadam, Generation of Genocchi polynomials of first order by recurrence relation, Fib. Quart. 2 (1992), 239-243. FORMULA E.g.f.: Sum((n, k=0..inf) T(n, k) t^k x^(2n)/(2n)! = cosh(sqrt(1+4t) x/2)/ cosh(x/2). T(k, n) = Sum[i=0..n-k, A028296(i)/4^(n-k)*C(2n, 2i)*C(n-l, n-k-l)], or 0 if n=0} (-1)^(n+k)*2^(n-k)*T(n, k) = A005647(n). Sum_{k>=0} (-1)^(n+k)*2^(2n-k)*T(n, k) = A000795(n). Sum_{k>=0} (-1)^(n+k)*T(n, k) = A006846(n), where A006846 = Hammersley's polynomial p_n(1). - Philippe Deléham, Feb 26 2004. Column sequences (without leading zeros) give, for k=1..10: A065547 (twice), A095652-9. Cf. A000795, A005647, A000035. See A085707 for unsigned and transposed version. See A098435 for negative values of n, k. Sequence in context: A264436 A122850 A132062 * A143333 A283798 A065551 Adjacent sequences:  A065544 A065545 A065546 * A065548 A065549 A065550 KEYWORD sign,tabl AUTHOR Wouter Meeussen, Dec 02 2001 EXTENSIONS Edited by Ralf Stephan, Sep 08 2004 STATUS approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)