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A084948 a(n) = Product_{i=0..n-1} (8*i+2). 12
1, 2, 20, 360, 9360, 318240, 13366080, 668304000, 38761632000, 2558267712000, 189311810688000, 15523568476416000, 1397121162877440000, 136917873961989120000, 14513294639970846720000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..330

FORMULA

a(n) = A084943(n)/A000142(n)*A000079(n) = 8^n*pochhammer(1/4, n) = 1/2*Gamma(n+1/4)*sqrt(2)*Gamma(3/4)*8^n/Pi.

a(n) = (-6)^n*Sum_{k=0..n} (4/3)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012

G.f.: 2/G(0), where G(k)= 1 + 1/(1 - 2*x*(8*k+2)/(2*x*(8*k+2) - 1 + 16*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013

From Ilya Gutkovskiy, Mar 23 2017: (Start)

E.g.f.: 1/(1 - 8*x)^(1/4).

a(n) ~ sqrt(2*Pi)*8^n*n^n/(exp(n)*n^(1/4)*Gamma(1/4)). (End)

MAPLE

a := n->product(8*i+2, i=0..n-1); [seq(a(j), j=0..30)];

MATHEMATICA

Table[8^n*Pochhammer[1/4, n], {n, 0, 20}] (* G. C. Greubel, Aug 18 2019 *)

PROG

(PARI) vector(20, n, n--; prod(k=0, n-1, 8*k+2)) \\ G. C. Greubel, Aug 18 2019

(MAGMA) [1] cat [(&*[8*k+2: k in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Aug 18 2019

(Sage) [product(8*k+2 for k in (0..n-1)) for n in (0..20)] # G. C. Greubel, Aug 18 2019

(GAP) List([0..20], n-> Product([0..n-1], k-> 8*k+2) ); # G. C. Greubel, Aug 18 2019

CROSSREFS

Cf. A000165, A008544, A001813, A047055, A047657, A084947, A084949.

Sequence in context: A104462 A060164 A267827 * A187661 A263207 A218306

Adjacent sequences:  A084945 A084946 A084947 * A084949 A084950 A084951

KEYWORD

easy,nonn

AUTHOR

Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003

STATUS

approved

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Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)