cp's OEIS Frontend

A335948 T(n, k) = denominator([x^k] b_n(x)), where b_n(x) = Sum_{k=0..n} binomial(n,k)* Bernoulli(k, 1/2)*x^(n-k). Triangle read by rows, for n >= 0 and 0 <= k <= n.

%I A335948 #9 Jul 02 2020 12:56:52
%S A335948 1,1,1,12,1,1,1,4,1,1,240,1,2,1,1,1,48,1,6,1,1,1344,1,16,1,4,1,1,1,
%T A335948 192,1,48,1,4,1,1,3840,1,48,1,24,1,3,1,1,1,1280,1,16,1,40,1,1,1,1,
%U A335948 33792,1,256,1,32,1,8,1,4,1,1,1,3072,1,256,1,32,1,8,1,12,1,1
%N A335948 T(n, k) = denominator([x^k] b_n(x)), where b_n(x) = Sum_{k=0..n} binomial(n,k)* Bernoulli(k, 1/2)*x^(n-k). Triangle read by rows, for n >= 0 and 0 <= k <= n.
%C A335948 See A335947 for formulas and references concerning the polynomials.
%e A335948 First few polynomials are:
%e A335948 b_0(x) = 1;
%e A335948 b_1(x) = x;
%e A335948 b_2(x) = -(1/12) + x^2;
%e A335948 b_3(x) = -(1/4)*x + x^3;
%e A335948 b_4(x) = (7/240) - (1/2)*x^2 + x^4;
%e A335948 b_5(x) = (7/48)*x - (5/6)*x^3 + x^5;
%e A335948 b_6(x) = -(31/1344) + (7/16)*x^2 - (5/4)*x^4 + x^6;
%e A335948 Triangle starts:
%e A335948 1;
%e A335948 1,     1;
%e A335948 12,    1,    1;
%e A335948 1,     4,    1,   1;
%e A335948 240,   1,    2,   1,  1;
%e A335948 1,     48,   1,   6,  1,  1;
%e A335948 1344,  1,    16,  1,  4,  1,  1;
%e A335948 1,     192,  1,   48, 1,  4,  1, 1;
%e A335948 3840,  1,    48,  1,  24, 1,  3, 1, 1;
%e A335948 1,     1280, 1,   16, 1,  40, 1, 1, 1, 1;
%e A335948 33792, 1,    256, 1,  32, 1,  8, 1, 4, 1, 1;
%Y A335948 Cf. A335947 (numerators), A157780 (column 0), A033469 (column 0 even indices only).
%K A335948 nonn,frac,tabl
%O A335948 0,4
%A A335948 _Peter Luschny_, Jul 01 2020