This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A231530 Real part of Product_{k=1..n} (k+I). 9
 1, 1, 1, 0, -10, -90, -730, -6160, -55900, -549900, -5864300, -67610400, -839594600, -11186357000, -159300557000, -2416003824000, -38894192662000, -662595375078000, -11911522255750000, -225382826562400000, -4477959179352100000, -93217812901913700000, -2029107997508660900000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Extension of factorial(n) to factim(n,m) defined by the recurrence a(0)=1, a(n)=a(n-1)*(n+m*I). Hence n! = factim(n,0), while the current sequence lists the real parts of factim(n,1). The imaginary parts are in A231531 and squares of magnitudes are in A101686. LINKS Stanislav Sykora, Table of n, a(n) for n = 0..440 FORMULA From Peter Luschny, Oct 23 2015 : (Start) a(n) = Re(I!*(n-I)!)*sinh(Pi)/Pi. a(n) = n!*[x^n](cos(log(1-x))/(1-x)). a(n) = Sum_{k=0..floor(n/2)} (-1)^(n+k)*Stirling1(n+1,2*k+1). a(n) = Re(rf(1+I,n)) where rf(k,n) is the rising factorial and I the imaginary unit. a(n) = (-1)^n*A009454(n+1). (End) EXAMPLE factim(5,1) = -90+190*I. Hence a(n) = -90. MAPLE seq(simplify(Re(I!*(n-I)!)*sinh(Pi)/Pi), n=0..22); # Peter Luschny, Oct 23 2015 MATHEMATICA Table[Re[Product[k+I, {k, n}]], {n, 0, 30}] (* Harvey P. Dale, Aug 04 2016 *) PROG (PARI) Factim(nmax, m)={local(a, k); a=vector(nmax); a[1]=1+0*I;   for (k=2, nmax, a[k]=a[k-1]*(k-1+m*I); ); return(a); } a = Factim(1000, 1); real(a) (Sage) A231530 = lambda n : rising_factorial(1-I, n).real() [A231530(n) for n in range(24)] # Peter Luschny, Oct 23 2015 CROSSREFS Cf. A231531 (imaginary parts), A101686 (squares of magnitudes), A009454. See A242651, A242652 for a pair of similar sequences. Sequence in context: A265325 A038726 A009454 * A242652 A162756 A199940 Adjacent sequences:  A231527 A231528 A231529 * A231531 A231532 A231533 KEYWORD sign,easy AUTHOR Stanislav Sykora, Nov 10 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.