A147585 a(1) = 1; a(n) = (7*n-9)*a(n-1) for n > 1.

1, 5, 60, 1140, 29640, 978120, 39124800, 1838865600, 99298742400, 6057223286400, 411891183475200, 30891838760640000, 2533130778372480000, 225448639275150720000, 21643069370414469120000, 2229236145152690319360000, 245215975966795935129600000, 28690269188115124410163200000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..340

Formula

a(n) = Product_{k=1..n-1} (7*k - 2). - Klaus Brockhaus, Nov 10 2008

a(n) = (5*7^(n-1)*Gamma(5/7+n))/Gamma(12/7). - Klaus Brockhaus, Nov 10 2008

a(n+1) = Sum_{k=0..n} A132393(n,k)*5^k*7^(n-k). - Philippe Deléham, Nov 09 2008

G.f.: x/(1-5x/(1-7x/(1-12x/(1-14x/(1-19x/(1-21x/(1-26x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-2)^n*Sum_{k=0..n} (7/2)^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

Sum_{n>=1} 1/a(n) = 1 + (e/7^2)^(1/7)*(Gamma(5/7) - Gamma(5/7, 1/7)). - Amiram Eldar, Dec 19 2022

Maple

seq( -7^n*pochhammer(-2/7, n)/2, n = 1..15); # G. C. Greubel, Dec 03 2019

Mathematica

Table[-7^n*Pochhammer[-2/7, n]/2, {n, 15}] (* G. C. Greubel, Dec 03 2019 *)

Prog

(Magma) [ n eq 1 select 1 else Self(n-1)*(7*n-9): n in [1..15] ]; // Klaus Brockhaus, Nov 10 2008
(Magma) [ 1 ] cat [ &*[ (5+7*k): k in [0..n-1] ]: n in [1..14] ]; // Klaus Brockhaus, Nov 10 2008
(PARI) {for(n=1, 15, print1(prod(k=1, n-1, 7*k-2, ), ", "))} \\ Klaus Brockhaus, Nov 10 2008
(SageMath) [-7^n*rising_factorial(-2/7, n)/2 for n in (1..15)] # G. C. Greubel, Dec 03 2019

Crossrefs

Cf. A048994, A132393.

Cf. A045754, A049209, A084947, A144739, A144827, A051188.

Sequence in context: A062980 A365557 A113665 * A138215 A207648 A349883

Adjacent sequences: A147582 A147583 A147584 * A147586 A147587 A147588

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Extensions

Edited by Klaus Brockhaus, Nov 10 2008

Status

approved