A126772 Padovan factorials: a(n) is the product of the first n terms of the Padovan sequence. Similar to the Fibonacci factorial.

1, 1, 1, 2, 4, 12, 48, 240, 1680, 15120, 181440, 2903040, 60963840, 1706987520, 63158538240, 3094768373760, 201159944294400, 17299755209318400, 1972172093862297600, 297797986173206937600, 59559597234641387520000

Offset

1,4

Links

Table of n, a(n) for n=1..21.

Ian Stewart, Tales of a Neglected Number

Ian Stewart, Tales of a Neglected Number, Mathematical Recreations, Scientific American, Vol. 274, No. 6 (1996), pp. 102-103.

Eric Weisstein's World of Mathematics, Padovan Sequence

E. Wilson, The Scales of Mt. Meru

Formula

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

Maple

From R. J. Mathar, Sep 14 2010: (Start)
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:
A126772 := proc(n) mul( A000931(i), i=5..n+4) ; end proc: seq(A126772(n), n=1..40) ; (End)

Mathematica

Rest[FoldList[Times, 1, LinearRecurrence[{0, 1, 1}, {1, 1, 1}, 30]]] (* Harvey P. Dale, Apr 29 2013 *)

Crossrefs

Cf. A000931, A003266, A060006, A253924.

Sequence in context: A098558 A152827 A030813 * A030949 A030888 A030801

Adjacent sequences: A126769 A126770 A126771 * A126773 A126774 A126775

Keyword

nonn,easy

Author

John Lien, Feb 17 2007

Extensions

More terms from R. J. Mathar, Sep 14 2010

Status

approved