A004986 - OEIS

%I #19 Sep 08 2022 08:44:33

%S 1,14,154,1540,14630,134596,1211364,10729224,93880710,813632820,

%T 6997242252,59794615608,508254232668,4300612737960,36248021648520,

%U 304483381847568,2550048322973382,21300403638954132,177503363657951100,1476080603050330200,12251469005317740660,101512171758346994040

%N a(n) = (2^n/n!) * Product_{k=0..n-1} (4*k + 7).

%H G. C. Greubel, <a href="/A004986/b004986.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (1 - 8*x)^(-7/4).

%F a(n) ~ 4/3*Gamma(3/4)^-1*n^(3/4)*2^(3*n)*{1 + 21/32*n^-1 - ...}.

%F D-finite with recurrence: n*a(n) +2*(-4*n-3)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020

%p seq(2^n/n!*mul(4*k + 7, k=0..n-1), n=0..30);

%t Table[2^n/n! Product[4k+7,{k,0,n-1}],{n,0,25}] (* _Harvey P. Dale_, Apr 26 2019 *)

%t Table[8^n*Pochhammer[7/4, n]/n!, {n,0,25}] (* _G. C. Greubel_, Aug 22 2019 *)

%o (PARI) a(n) = 2^n*prod(k=0,n-1, 4*k+7)/n!;

%o vector(25, n, n--; a(n)) \\ _G. C. Greubel_, Aug 22 2019

%o (Magma) [1] cat [2^n*(&*[4*k+7: k in [0..n-1]])/Factorial(n): n in [1..25]]; // _G. C. Greubel_, Aug 22 2019

%o (Sage) [8^n*rising_factorial(7/4, n)/factorial(n) for n in (0..25)] # _G. C. Greubel_, Aug 22 2019

%o (GAP) List([0..25], n-> 2^n*Product([0..n-1], k-> 4*k+7)/Factorial(n) ); # _G. C. Greubel_, Aug 22 2019

%K nonn,easy

%O 0,2

%A Joe Keane (jgk(AT)jgk.org)

%E More terms from _Sascha Kurz_, Mar 24 2002