A058940 Triangle of coefficients of Euler polynomials rescaled to integers by multiplication with 2^(binary carry sequence (A007814)).

1, -1, 2, 0, -1, 1, 1, 0, -6, 4, 0, 1, 0, -2, 1, -1, 0, 5, 0, -5, 2, 0, -3, 0, 5, 0, -3, 1, 17, 0, -84, 0, 70, 0, -28, 8, 0, 17, 0, -28, 0, 14, 0, -4, 1, -31, 0, 153, 0, -126, 0, 42, 0, -9, 2, 0, -155, 0, 255, 0, -126, 0, 30, 0, -5, 1, 691, 0, -3410, 0, 2805, 0, -924, 0, 165, 0, -22, 4, 0, 2073, 0, -3410, 0, 1683, 0, -396, 0, 55, 0, -6

Offset: 0

Author

Wouter Meeussen, Jan 12 2001

Keywords

• tabl
• nice
• sign

Comments

Sums of even rows are A002425, sums of odd rows are 0, first element of even rows is -row sum, first element of row(2^p) is second element of row(1+2^p), LCM of numerators of Euler polynomial coefficients is A007814.

Crossrefs

Cf. A004174, A002425, A007814.

Programs

Maple

A058940_row := proc(n) local i; seq(coeff(euler(n,x)*2^padic[ordp](n+1,2),x,i), i=0..n) end: # Peter Luschny, Nov 26 2010

Mathematica

Flatten[ Table[ CoefficientList[ EulerE[n, x]*2^IntegerExponent[n+1, 2], x], {n, 0, 12}]] (* Jean-François Alcover, Nov 18 2011, after Wouter Meeussen *)

Formula

T(n, k) = [x^k] E(n, x)*2^A007814(n+1).