A281825 Numerators of the binomial transform of A198631(n)/A006519(n+1) with A198631(1) = -1 instead of 1.
1, 1, 0, -3, -2, -7, -4, -23, -6, -45, -8, 655, -10, -5483, -12, 929361, -14, -3202321, -16, 221930513, -18, -4722116559, -20, 968383680659, -22, -14717667114197, -24, 2093660879252571, -26, -86125672563201235, -28, 129848163681107301025, -30
Offset: 0
Keywords
Programs
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Maple
A198631 := proc(n) 1/(1+exp(-x)) ; coeftayl(%,x=0,n) ; numer(%*n!) ; end proc: A006519 := proc(n) 2^padic[ordp](n,2) ; end proc: L := [seq( A198631(n)/A006519(n+1),n=0..40)] ; subsop(2=-1/2,L) ; b := BINOMIAL(%) ; for i from 1 to nops(b) do printf("%d,",numer(b[i])) ; end do: # R. J. Mathar, Feb 21 2017
Formula
By definition f(0) - c(0), f(1) + c(1), f(2) - c(2), f(3) + c(3), ... is an autosequence of the first kind, here 1 - 1 = 0, 1/2 - 1/2 = 0, 0 - 0 = 0, -3/4 - 1/4 = -1, -2 - 0 = -2, -7/2 + 1/2 = -3, ... i.e., t(n) = 0, 0, followed by -A001477(n), not in the OEIS, but the corresponding autosequence of the second kind is: A199969 = 0, 0, -2, -3, -4, ... Hence f(n) from c(n) and t(n).
Comments