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%I #27 Mar 02 2024 13:56:07
%S 1,1,1,2,4,12,48,240,1680,15120,181440,2903040,60963840,1706987520,
%T 63158538240,3094768373760,201159944294400,17299755209318400,
%U 1972172093862297600,297797986173206937600,59559597234641387520000
%N Padovan factorials: a(n) is the product of the first n terms of the Padovan sequence. Similar to the Fibonacci factorial.
%H Ian Stewart, <a href="https://web.archive.org/web/20120330094207/http://www.fortunecity.com/emachines/e11/86/padovan.html">Tales of a Neglected Number</a>
%H Ian Stewart, <a href="https://www.jstor.org/stable/24989576">Tales of a Neglected Number</a>, Mathematical Recreations, Scientific American, Vol. 274, No. 6 (1996), pp. 102-103.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PadovanSequence.html">Padovan Sequence</a>
%H E. Wilson, <a href="http://www.anaphoria.com/meruone.PDF">The Scales of Mt. Meru</a>
%F a(n) ~ c * d^(n/2) * r^(n^2/2), where r = 1.324717957244746... (see A060006) is the root of the equation r^3 = r + 1, d = 0.393641282401116385386658448446561... is the root of the equation 1 + 7*d + 184*d^2 - 529*d^3 = 0, c = 1.25373683131537208838997864311903035079685338006712312402418098138010834953... (see A253924). - _Vaclav Kotesovec_, Jan 26 2015
%p From _R. J. Mathar_, Sep 14 2010: (Start)
%p A000931 := proc(n) option remember; if n = 0 then 1; elif n <=2 then 0; else procname(n-2)+procname(n-3) ; end if; end proc:
%p A126772 := proc(n) mul( A000931(i),i=5..n+4) ; end proc: seq(A126772(n),n=1..40) ; (End)
%t Rest[FoldList[Times,1,LinearRecurrence[{0,1,1},{1,1,1},30]]] (* _Harvey P. Dale_, Apr 29 2013 *)
%Y Cf. A000931, A003266, A060006, A253924.
%K nonn,easy
%O 1,4
%A _John Lien_, Feb 17 2007
%E More terms from _R. J. Mathar_, Sep 14 2010
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