A370691 Square array read by upward antidiagonals: T(n, k) = denominator( 2*k!*(-2)^k*Sum_{m=1..n}( 1/(2*m-1)^(k+1) ) ).
1, 1, 1, 3, 1, 1, 15, 9, 1, 1, 105, 225, 27, 1, 765765, 405810405, 91398648466125, 48049812916875, 1033788065625, 89339709375, 3796875, 729, 1, 1, 1, 315, 11025, 3375, 27, 1, 1, 3465, 99225, 1157625, 16875, 81, 1, 1, 45045, 12006225, 31255875, 40516875, 253125, 243, 1, 1, 45045, 2029052025
Offset: 0
Examples
array begins: 1, 1, 1, 1, 1, 1 1, 1, 1, 1, 1, 1 3, 9, 27, 27, 81, 243 15, 225, 3375, 16875, 253125, 759375 105, 11025, 1157625, 40516875, 4254271875, 89339709375 315, 99225, 31255875, 3281866875, 1033788065625, 65128648134375 3465, 12006225, 41601569625, 48049812916875, 166492601756971875, 115379373017581509375
Crossrefs
Programs
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Maple
A := (n, k) -> Psi(k, n + 1/2) - Psi(k, 1/2): seq(lprint(seq(denom(A(n, k)), k = 0..4)), n=0..6);
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PARI
T(n, k) = denominator(sum(m=1, n, 1/(2*m-1)^(k+1))*k!*(-2)^k*2)