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 A281964 Real part of n!*Sum_{k=1..n} i^(k-1)/k, where i is sqrt(-1). 5
 1, 2, 4, 16, 104, 624, 3648, 29184, 302976, 3029760, 29698560, 356382720, 5111976960, 71567677440, 986336870400, 15781389926400, 289206418636800, 5205715535462400, 92506221468057600, 1850124429361152000, 41285515024760832000, 908281330544738304000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Iain Fox, Table of n, a(n) for n = 1..450 (first 100 terms from Daniel Suteu) FORMULA a(n) ~ Pi/4 * n!. a(1) = 1, a(n+1) = a(n)*(n+1) + n!*cos(Pi*n/2). E.g.f.: arctan(x)/(1 - x). - Ilya Gutkovskiy, Dec 19 2017 EXAMPLE For n=5, a(5) = 104, which is the real part of 5!*(1/1 + i/2 - 1/3 - i/4 + 1/5) = 104+30*i. PROG (PARI) a(n) = real(n!*sum(k=1, n, I^(k-1)/k)); (PARI) first(n) = x='x+O('x^(n+1)); Vec(serlaplace(atan(x)/(1 - x))) \\ Iain Fox, Dec 19 2017 CROSSREFS The corresponding imaginary part is A282132. Cf. A003881, A024167. Sequence in context: A066318 A308606 A066952 * A297009 A135249 A318154 Adjacent sequences: A281961 A281962 A281963 * A281965 A281966 A281967 KEYWORD nonn AUTHOR Daniel Suteu, Feb 06 2017 STATUS approved

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Last modified October 3 07:13 EDT 2023. Contains 365842 sequences. (Running on oeis4.)