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A342177 Product of first n Motzkin numbers. 1
1, 1, 2, 8, 72, 1512, 77112, 9793224, 3163211352, 2641281478920, 5779123875876960, 33507360232334614080, 519732664563742198994880, 21743016022024154894950804800, 2470745882646692817332839752643200, 767344490265348681664694707657903910400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

Eric Weisstein's World of Mathematics, Motzkin Number.

FORMULA

a(n) = Product_{k=1..n} A001006(k).

a(n) ~ c * 3^(n*(n+4)/2) * exp(3*n/2) / (2^(n + 3/4) * Pi^(n/2 + 3/4) * n^(3*n/2 + 51/16)), where c = 1.88710807429950713889649869555827071385924787813206239984338608598135477864...

MAPLE

b:= proc(n) option remember; `if`(n<2, 1,

      ((2*n+1)*b(n-1) +(3*n-3)*b(n-2))/(n+2))

    end:

a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:

seq(a(n), n=0..18);  # Alois P. Heinz, Mar 04 2021

MATHEMATICA

Table[Product[Hypergeometric2F1[(1-k)/2, -k/2, 2, 4], {k, 1, n}], {n, 0, 15}]

FoldList[Times, 1, Table[Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4], {n, 1, 15}]]

CROSSREFS

Cf. A001006, A342170.

Sequence in context: A038057 A107270 A294351 * A125814 A295044 A305000

Adjacent sequences:  A342174 A342175 A342176 * A342178 A342179 A342180

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 04 2021

STATUS

approved

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Last modified November 29 05:05 EST 2021. Contains 349416 sequences. (Running on oeis4.)