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A231531 Imaginary parts of a(0)=1, a(n)=Prod_{k=1..n}(k+I). 7
0, 1, 3, 10, 40, 190, 1050, 6620, 46800, 365300, 3103100, 28269800, 271627200, 2691559000, 26495469000, 238131478000, 1394099824000, -15194495654000, -936096296850000, -29697351895900000, -819329864480400000, -21683886333440500000, -570263312237604700000, -15145164178973569000000, -409583160925827252000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 links the imaginary parts of factim(n,1). The real parts are in A231530 and squares of magnitudes are in A101686.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..440

EXAMPLE

factim(5,1) = -90+190*I. Hence a(5) = 190.

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); imag(a)

CROSSREFS

Cf. A231530 (real parts), A101686 (squares of magnitudes).

Sequence in context: A217885 A216367 A003703 * A136128 A089902 A093133

Adjacent sequences:  A231528 A231529 A231530 * A231532 A231533 A231534

KEYWORD

sign,easy

AUTHOR

Stanislav Sykora, Nov 10 2013

STATUS

approved

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Last modified April 17 20:01 EDT 2014. Contains 240655 sequences.