login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034301 a(n) = n-th quintic factorial number divided by 4. 15
1, 9, 126, 2394, 57456, 1666224, 56651616, 2209413024, 97214173056, 4763494479744, 257228701906176, 15176493412464384, 971295578397720576, 67019394909442719744, 4959435223298761261056, 391795382640602139623424, 32910812141810579728367616, 2929062280621141595824717824 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..350

FORMULA

a(n) = A008546(n)/4.

4*a(n) = (5*n-1)(!^5) = Product_{j=1..n} (5*j-1).

a(n) = (5*n)!/(5^n*n!*A008548(n)*2*A034323(n)*3*A034300(n)).

E.g.f.: (-1 + (1-5*x)^(-4/5))/4, a(0) = 0.

a(n) ~ sqrt(2*Pi) * 5/(4*Gamma(4/5)) * n^(13/10) * (5*n/e)^n * (1 + (241/300)/n + ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

D-finite with recurrence: a(n) +(-5*n+1)*a(n-1)=0. - R. J. Mathar, Feb 20 2020

MAPLE

a:= n-> mul(5*k-1, k=1..n)/4: seq(a(n), n=1..20); # G. C. Greubel, Aug 23 2019

MATHEMATICA

Table[-5^(n+1)*Pochhammer[-1/5, n+1]/4, {n, 20}] (* G. C. Greubel, Aug 23 2019 *)

PROG

(PARI) a(n) = prod(k=1, n, 5*k-1)/4;

vector(20, n, a(n)) \\ G. C. Greubel, Aug 23 2019

(MAGMA) [&*[5*k-1: k in [1..n]]/4: n in [1..20]]; // G. C. Greubel, Aug 23 2019

(Sage) [-5^(n+1)*rising_factorial(-1/5, n+1)/4 for n in (1..20)] # G. C. Greubel, Aug 23 2019

(GAP) List([1..20], n-> Product([1..n], k-> 5*k-1)/4 ); # G. C. Greubel, Aug 23 2019

CROSSREFS

Cf. A008546, A008548, A034300, A025750.

Sequence in context: A306033 A065707 A338077 * A092651 A258294 A073014

Adjacent sequences:  A034298 A034299 A034300 * A034302 A034303 A034304

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

EXTENSIONS

Terms a(17) onward added by G. C. Greubel, Aug 23 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 20:32 EDT 2021. Contains 348034 sequences. (Running on oeis4.)