login
A233508
Numerators of the triangle of polynomial coefficients P(0,x)=1, 2*P(n)=(1+x)*((1+x)^(n-1)+x^(n-1)). Of the first array of A133135.
2
1, 1, 1, 1, 3, 1, 1, 3, 2, 1, 1, 2, 3, 5, 1, 1, 5, 5, 5, 3, 1, 1, 3, 15, 10, 15, 7, 1, 1, 7, 21, 35, 35, 21, 4, 1, 1, 4, 14, 28, 35, 28, 14, 9, 1, 1, 9, 18, 42, 63, 63, 42, 18, 5, 1, 1, 5, 45, 60, 105, 126, 105, 60, 45, 11, 1
OFFSET
0,5
COMMENTS
Discovered via Euler polynomials A060096(n)/A060097(n).
The fractional sequence is 1, 1, 1, 1/2, 3/2, 1, 1/2, 3/2, 2, 1, 1/2, 2, 3, 5/2, 1,... =a(n)/b(n). There is a correspondant sequence for Bernoulli polynomials (*).
FORMULA
a(n) = reduced A133138(n)/A007395.
EXAMPLE
1,
1, 1,
1, 3, 1,
1, 3, 2, 1,
1, 2, 3, 5, 1,
1, 5, 5, 5, 3, 1, etc.
MATHEMATICA
p[n_] := (1+x)*((1+x)^(n-1)+x^(n-1))/2; t[n_, k_] := Coefficient[p[n], x, k] // Numerator; Table[t[n, k], {n, 0, 10 }, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 16 2013 *)
CROSSREFS
Cf. (*) A193815.
Sequence in context: A137728 A054398 A093415 * A106749 A225224 A140216
KEYWORD
nonn,tabl,frac
AUTHOR
Paul Curtz, Dec 11 2013
STATUS
approved