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A231531 Imaginary part of Prod_{k=1..n}(k+I). 8
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 shows 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).

See A242651, A242652 for a pair of similar sequences.

Sequence in context: A216367 A003703 A242651 * 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 October 23 00:52 EDT 2014. Contains 248411 sequences.