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A318143 Coefficients of the polynomials generated by the e.g.f. cosh(x*z)*(x-1)/(x-exp(z*(x-1))), triangle read by rows, T(n,k) for 0 <= k <= n.

%I A318143 #6 Aug 19 2018 11:55:22
%S A318143 1,1,0,1,1,1,1,4,4,0,1,11,17,7,1,1,26,76,66,16,0,1,57,317,467,237,31,
%T A318143 1,1,120,1212,2962,2612,806,64,0,1,247,4321,17215,24145,13519,2641,
%U A318143 127,1,1,502,14644,92554,199192,178486,65884,8434,256,0
%N A318143 Coefficients of the polynomials generated by the e.g.f. cosh(x*z)*(x-1)/(x-exp(z*(x-1))), triangle read by rows, T(n,k) for 0 <= k <= n.
%e A318143 [n\k][0,   1,    2,     3,     4,     5,    6,   7,  8]
%e A318143 [0]   1;
%e A318143 [1]   1,   0;
%e A318143 [2]   1,   1,    1;
%e A318143 [3]   1,   4,    4,     0;
%e A318143 [4]   1,  11,   17,     7,     1;
%e A318143 [5]   1,  26,   76,    66,    16,     0;
%e A318143 [6]   1,  57,  317,   467,   237,    31,    1;
%e A318143 [7]   1, 120, 1212,  2962,  2612,   806,   64,   0;
%e A318143 [8]   1, 247, 4321, 17215, 24145, 13519, 2641, 127, 1;
%p A318143 gf := cosh(x*z)*(x-1)/(x-exp(z*(x-1))):
%p A318143 ser := series(gf, z, 12): p := n -> normal(n!*coeff(ser, z, n)):
%p A318143 seq(seq(coeff(p(n),x,k), k=0..n), n=0..10);
%Y A318143 Row sums are (-1)^n*A009179(n).
%Y A318143 Alternating row sums are 1.
%Y A318143 Polynomials evaluated at x = 0 are 1.
%Y A318143 T(n, n-1) = A051049(n-1) for n >= 1.
%Y A318143 T(n, 1) = A000295(n) for n >= 0.
%Y A318143 Cf. A046802, A173018.
%K A318143 nonn,tabl
%O A318143 0,8
%A A318143 _Peter Luschny_, Aug 19 2018