A336454
a(n) = denominator(2^n*Sum_{k=0..n} binomial(n, k)*Bernoulli(k, 1/2)*x^(n-k)).
Original entry on oeis.org
1, 1, 3, 1, 15, 3, 21, 3, 15, 5, 33, 3, 1365, 105, 15, 3, 255, 15, 1995, 105, 1155, 165, 345, 15, 1365, 273, 21, 7, 435, 15, 7161, 231, 19635, 1785, 105, 3, 959595, 25935, 1365, 105, 47355, 1155, 49665, 1155, 2415, 2415, 4935, 105, 23205, 3315, 7293, 429, 8745
Offset: 0
-
Bcp := n -> 2^n*add(binomial(n, k)*bernoulli(k, 1/2)*x^(n-k), k=0..n):
a := n -> denom(Bcp(n)): seq(a(n), n=0..52);
A335953
T(n, k) = numerator([x^k] b_n(x)), where b_n(x) = Sum_{k=0..n} binomial(n,k)*2^k* Bernoulli(k, 1/2)*x^(n-k). Triangle read by rows, for n >= 0 and 0 <= k <= n.
Original entry on oeis.org
1, 0, 1, -1, 0, 1, 0, -1, 0, 1, 7, 0, -2, 0, 1, 0, 7, 0, -10, 0, 1, -31, 0, 7, 0, -5, 0, 1, 0, -31, 0, 49, 0, -7, 0, 1, 127, 0, -124, 0, 98, 0, -28, 0, 1, 0, 381, 0, -124, 0, 294, 0, -12, 0, 1, -2555, 0, 381, 0, -310, 0, 98, 0, -15, 0, 1
Offset: 0
[0] 1
[1] 0, 1
[2] -1, 0, 1
[3] 0, -1, 0, 1
[4] 7, 0, -2, 0, 1
[5] 0, 7, 0, -10, 0, 1
[6] -31, 0, 7, 0, -5, 0, 1
[7] 0, -31, 0, 49, 0, -7, 0, 1
[8] 127, 0, -124, 0, 98, 0, -28, 0, 1
[9] 0, 381, 0, -124, 0, 294, 0, -12, 0, 1
-
Bcn := n -> 2^n*bernoulli(n, 1/2):
Bcp := n -> add(binomial(n, k)*Bcn(k)*x^(n-k), k=0..n):
polycoeff := p -> seq(numer(coeff(p, x, k)), k = 0..degree(p, x)):
Trow := n -> polycoeff(Bcp(n)): seq(print(Trow(n)), n=0..9);
Showing 1-2 of 2 results.