A227608 Denominators of A225825(n) difference table written by antidiagonals.

1, 2, 2, 6, 3, 6, 2, 3, 3, 2, 30, 15, 15, 15, 30, 2, 15, 15, 15, 15, 2, 42, 21, 105, 105, 105, 21, 42, 2, 21, 21, 105, 105, 21, 21, 2, 30, 15, 105, 105, 105, 105, 105, 15, 30, 2, 15, 15, 105, 105, 105, 105, 15, 15, 2, 66, 33, 165, 165, 1155, 231, 1155, 165, 165, 33, 66, 2, 33, 33, 165, 165, 231, 231, 165, 165, 33, 33, 2

Offset

0,2

Links

Table of n, a(n) for n=0..77.

Example

1,
-1/2,      1/2,
-1/6,     -2/3,     -1/6,
1/2,       1/3,     -1/3,     -1/2,
7/30,    11/15,    16/15,    11/15,     7/30,
-3/2,   -19/15,    -8/15,     8/15,    19/15,    3/2,
-31/42, -47/21, -368/105, -424/105, -368/105, -47/21, -31/42.
Row sums: 1, 0/2, -6/6, 0/6, 90/30, 0/30, -3570/210, 0/210, 32550/210,... .
Are the denominators A034386(n+1)?
Reduced row sums: 1, 0, -1, 0, 3, 0, -17, 0, 155,... = -A036968(n+1)? See A226158(n+2). First 100 terms checked by Jean-François Alcover.

Mathematica

max = 12; b[0] = 1; b[n_] := Numerator[ BernoulliB[n, 1/2] - (n+1)*EulerE[n, 0]]; t = Table[b[n], {n, 0, max}] / Table[ Sum[ Boole[ PrimeQ[d+1]]/(d+1), {d, Divisors[n]}] // Denominator, {n, 0, max}]; dt = Table[ Differences[t, n], {n, 0, max}]; Table[ dt[[n-k+1, k]] // Denominator, {n, 1, max}, {k, 1, n}] // Flatten (* Jean-François Alcover, Aug 12 2013 *)

Crossrefs

Cf. A085738

Sequence in context: A275037 A174833 A085738 * A276484 A100641 A028421

Adjacent sequences: A227605 A227606 A227607 * A227609 A227610 A227611

Keyword

nonn,frac,tabl

Author

Paul Curtz, Aug 10 2013

Extensions

More terms from Jean-François Alcover, Aug 12 2013

Status

approved