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A126772 Padovan factorials: a(n) is the product of the first n terms of the Padovan sequence. Similar to the Fibonacci factorial. 8
1, 1, 1, 2, 4, 12, 48, 240, 1680, 15120, 181440, 2903040, 60963840, 1706987520, 63158538240, 3094768373760, 201159944294400, 17299755209318400, 1972172093862297600, 297797986173206937600, 59559597234641387520000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

I. Stewart, Tales of a Neglected Number

Eric Weisstein's World of Mathematics, Padovan Sequence

E. Wilson, The Scales of Mt. Meru

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).

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

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Last modified April 15 17:25 EDT 2021. Contains 342977 sequences. (Running on oeis4.)