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A084947 a(n) = Product_{i=0..n-1} (7*i+2). 22
1, 2, 18, 288, 6624, 198720, 7352640, 323516160, 16499324160, 956960801280, 62202452083200, 4478576549990400, 353807547449241600, 30427449080634777600, 2829752764499034316800, 282975276449903431680000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..340

FORMULA

a(n) = A084942(n)/A000142(n)*A000079(n) = 7^n*pochhammer(2/7, n) = 7^n*Gamma(n+2/7)/Gamma(2/7).

a(0) = 1; a(n) = (7*n - 5)*a(n-1) for n > 0. - Klaus Brockhaus, Nov 10 2008

G.f.: 1/(1-2*x/(1-7*x/(1-9*x/(1-14*x/(1-16*x/(1-21*x/(1-23*x/(1-28*x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-5)^n*Sum_{k=0..n} (7/5)^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

From Ilya Gutkovskiy, Mar 23 2017: (Start)

E.g.f.: 1/(1 - 7*x)^(2/7).

a(n) ~ sqrt(2*Pi)*7^n*n^n/(exp(n)*n^(3/14)*Gamma(2/7)). (End)

MAPLE

a := n->product(7*i+2, i=0..n-1); [seq(a(j), j=0..30)];

MATHEMATICA

Join[{1}, FoldList[Times, 7*Range[0, 15]+2]] (* Harvey P. Dale, Nov 27 2015 *)

Table[7^n*Pochhammer[2/7, n], {n, 0, 15}] (* G. C. Greubel, Aug 18 2019 *)

PROG

(MAGMA) [ 1 ] cat [ &*[ (7*k+2): k in [0..n-1] ]: n in [1..15] ]; // Klaus Brockhaus, Nov 10 2008

(PARI) vector(20, n, n--; prod(k=0, n-1, 7*k+2)) \\ G. C. Greubel, Aug 18 2019

(Sage) [product(7*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-> 7*k+2) ); # G. C. Greubel, Aug 18 2019

CROSSREFS

Cf. A000165, A008544, A001813, A045754, A047055, A047657, A084947, A084948, A084949, A144739, A144827, A049209, A051188.

Sequence in context: A294193 A127134 A131455 * A123385 A121564 A224384

Adjacent sequences:  A084944 A084945 A084946 * A084948 A084949 A084950

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

a(15) from Klaus Brockhaus, Nov 10 2008

STATUS

approved

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Last modified December 11 07:41 EST 2019. Contains 329914 sequences. (Running on oeis4.)