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 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 (list; table; graph; refs; listen; history; text; internal format)
 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 (*). LINKS 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 Adjacent sequences:  A233505 A233506 A233507 * A233509 A233510 A233511 KEYWORD nonn,tabl,frac AUTHOR Paul Curtz, Dec 11 2013 STATUS approved

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Last modified June 20 15:04 EDT 2021. Contains 345165 sequences. (Running on oeis4.)