bibkey: lang2014a238474
authors: Wolfdieter Lang
year: 2014
title: "OEIS A238474: a signed factorial quotient"
doi: null
url: https://oeis.org/A238474
claim: "For every natural m, A238474(m)=(-1)^m*(m+3)!/(2*(m+1)), with sequence offset zero."
strata_touched:
  - D5/S3/Combinatorics/Derangements/AdjacentDifferenceRefutation
license: citation-only
triage: anchor

The auxiliary sequence A238474

Verified locator

Source: https://oeis.org/A238474

The internal entry, revision 15, gives the FORMULA line:

a(n) = (-1)^n*(n+3)!/(2*(n+1)) for n >= 0

The offset is 0,1; the author line is Wolfdieter Lang, 1 March 2014. The history and formula are the source for the total rational function AdjacentDifferenceRefutation.b. Its denominator is nonzero for every natural input. In particular, $b(0)=3$ and $b(1)=-6$.

The literal A378495 question substitutes $m=n-4$ for every $n\ge 4$. At $n=5$ the required absolute value is therefore 6. This source identity does not itself say anything about derangement triangle cardinalities; their comparison is a separate question in Kagey’s note.

The bounded source qualification recorded in #23900 read revision 15, its formula, offset and history. The rational formula is used directly, with no integer-division or integrality premise and no shift correction. No global literature-completeness claim is made.