A027537 Square of the lower triangular normalized Eulerian number matrix.

1, 3, 1, 19, 16, 1, 201, 319, 55, 1, 3131, 8296, 2816, 156, 1, 66883, 274089, 158774, 18254, 399, 1, 1866103, 11233692, 10137723, 2064028, 99093, 960, 1, 65599089, 559402687, 738815949, 240080355, 21320275, 481821, 2223, 1, 2826880471

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Formula

Numerators of lower triangle of (a[ i, j ])^2 where a[ i, j ] = A(i, j)/i! if j<=i, 0 if j>i

Mathematica

rows = 9; t[n_, k_] := Sum[(-1)^j*(k - j)^n*Binomial[n + 1, j], {j, 0, k}]; m = Table[If[k <= n, t[n, k]/n!, 0], {n, 1, rows}, {k, 1, rows}]; m2 = m.m; Table[fracs = m2[[i]]; nums = fracs // Numerator; dens = fracs // Denominator; lcm = LCM @@ dens; Table[nums[[j]]*lcm/dens[[j]], {j, 1, i}], {i, 1, rows}] // Flatten (* Jean-François Alcover, Mar 05 2013 *)

Crossrefs

Cf. A008292.

Sequence in context: A247232 A147076 A372175 * A192721 A370949 A002380

Adjacent sequences: A027534 A027535 A027536 * A027538 A027539 A027540

Keyword

nonn,tabl

Author

Olivier Gérard

Status

approved