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A004997 a(n) = (6^n/n!) * Product_{k=0..n-1} (6*k + 7). 1

%I #23 Sep 08 2022 08:44:33

%S 1,42,1638,62244,2334150,86830380,3212724060,118411829640,

%T 4351634739270,159559940439900,5839893820100340,213421574152757880,

%U 7789887456575662620,284031281108989544760,10346853811827476273400,376625478750520136351760,13699751789550169959795270

%N a(n) = (6^n/n!) * Product_{k=0..n-1} (6*k + 7).

%H G. C. Greubel, <a href="/A004997/b004997.txt">Table of n, a(n) for n = 0..635</a>

%F G.f.: (1 - 36*x)^(-7/6).

%F a(n) ~ 6*Gamma(1/6)^-1*n^(1/6)*6^(2*n)*(1 + (7/72)*n^-1 - ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

%F D-finite with recurrence: n*a(n) +6*(-6*n-1)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020

%p a:= n-> (6^n/n!)*mul(6*k+7, k=0..n-1); seq(a(n), n=0..20); # _G. C. Greubel_, Aug 22 2019

%t Table[6^(2*n)*Pochhammer[7/6, n]/n!, {n,0,20}] (* _G. C. Greubel_, Aug 22 2019 *)

%o (PARI) a(n) = 6^n*prod(k=0,n-1, 6*k+7)/n!;

%o vector(20, n, a(n-1)) \\ _G. C. Greubel_, Aug 22 2019

%o (Magma) [1] cat [6^n*&*[6*k+7: k in [0..n-1]]/Factorial(n): n in [1..20]]; // _G. C. Greubel_, Aug 22 2019

%o (Sage) [6^(2*n)*rising_factorial(7/6, n)/factorial(n) for n in (0..20)] # _G. C. Greubel_, Aug 22 2019

%o (GAP) List([0..20], n-> 6^n*Product([0..n-1], k-> 6*k+7)/Factorial(n) ); # _G. C. Greubel_, Aug 22 2019

%K nonn,easy

%O 0,2

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

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)