A144827 Partial products of successive terms of A017029; a(0)=1.

1, 4, 44, 792, 19800, 633600, 24710400, 1136678400, 60243955200, 3614637312000, 242180699904000, 17921371792896000, 1451631115224576000, 127743538139762688000, 12135636123277455360000, 1237834884574300446720000, 134924002418598748692480000, 15651184280557454848327680000

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..100

Formula

a(n) = Sum_{k=0..n} A132393(n,k)*4^k*7^(n-k).

G.f.: 1/(1-4*x/(1-7*x/(1-11*x/(1-14*x/(1-18*x/(1-21*x/(1-25*x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-3)^n*Sum_{k=0..n} (7/3)^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

From Ilya Gutkovskiy, Mar 23 2017: (Start)

E.g.f.: 1/(1 - 7*x)^(4/7).

a(n) ~ sqrt(2*Pi)*7^n*n^(n+1/14)/(exp(n)*Gamma(4/7)). (End)

a(n) = 4*7^(n-1)*Pochhammer(n-1, 11/7) with a(0) = 1. - G. C. Greubel, Feb 22 2022

Sum_{n>=0} 1/a(n) = 1 + (e/7^3)^(1/7)*(Gamma(4/7) - Gamma(4/7, 1/7)). - Amiram Eldar, Dec 19 2022

Example

a(0)=1, a(1)=4, a(2)=4*11=44, a(3)=4*11*18=792, a(4)=4*11*18*25=19800, ...

Mathematica

FoldList[Times, 1, Range[4, 150, 7]] (* Harvey P. Dale, Apr 25 2014 *)

Prog

(Magma) [ 1 ] cat [ &*[ (7*k+4): k in [0..n] ]: n in [0..14] ]; // Klaus Brockhaus, Nov 10 2008
(SageMath) [1]+[4*7^(n-1)*rising_factorial(11/7, n-1) for n in (1..30)] # G. C. Greubel, Feb 22 2022

Crossrefs

Cf. A001715, A002866, A007559, A008546, A045754, A047053, A132393.

Cf. A049209, A049308, A051188, A084947, A144739, A147585.

Sequence in context: A157093 A365556 A088594 * A354260 A337777 A375872

Adjacent sequences: A144824 A144825 A144826 * A144828 A144829 A144830

Keyword

nonn

Author

Philippe Deléham, Sep 21 2008

Extensions

Corrected a(9) by Vincenzo Librandi, Jul 14 2011

Status

approved