cp's OEIS Frontend

A214407 Triangle read by rows. The coefficients in ascending order of x^i of the polynomials p{0}(x) = 1 and p{n}(x) = Sum_{k=0..n-1; k even} binomial(n, k) * p{k}(0)*(1 - n%2 + x^(n - k)).

%I A214407 #12 May 06 2023 09:01:45
%S A214407 1,0,1,1,0,1,0,3,0,1,7,0,6,0,1,0,35,0,10,0,1,121,0,105,0,15,0,1,0,847,
%T A214407 0,245,0,21,0,1,3907,0,3388,0,490,0,28,0,1,0,35163,0,10164,0,882,0,36,
%U A214407 0,1,202741,0,175815,0,25410,0,1470,0,45,0,1,0
%N A214407 Triangle read by rows. The coefficients in ascending order of x^i of the polynomials p{0}(x) = 1 and p{n}(x) = Sum_{k=0..n-1; k even} binomial(n, k) * p{k}(0)*(1 - n%2 + x^(n - k)).
%C A214407 Matrix inverse of a signed variant of A119467.
%F A214407 T(n, k) = n! * [y^k] [x^n] (exp(x * y) / (2 - cosh(x))). - _Peter Luschny_, May 06 2023
%e A214407 1
%e A214407 0, 1
%e A214407 1, 0, 1
%e A214407 0, 3, 0, 1
%e A214407 7, 0, 6, 0, 1
%e A214407 0, 35, 0, 10, 0, 1
%e A214407 121, 0, 105, 0, 15, 0, 1
%e A214407 0, 847, 0, 245, 0, 21, 0, 1
%e A214407 3907, 0, 3388, 0, 490, 0, 28, 0, 1
%o A214407 (Sage)
%o A214407 @CachedFunction
%o A214407 def A214407_poly(n, x) :
%o A214407     return 1 if n==0 else add(A214407_poly(k, 0)*binomial(n, k)*(x^(n-k)+1-n%2) for k in range(n)[::2])
%o A214407 def A214407_row(n) :
%o A214407     R = PolynomialRing(ZZ, 'x')
%o A214407     return R(A214407_poly(n,x)).coeffs()
%o A214407 for n in (0..8) : A214407_row(n)
%Y A214407 Cf. A119467, A327034 (row sums), A094088 (column 0).
%K A214407 nonn,tabl
%O A214407 0,8
%A A214407 _Peter Luschny_, Jul 16 2012