cp's OEIS Frontend

A216703 a(n) = Product_{k=1..n} (49 - 7/k).

%I A216703 #32 Aug 17 2025 03:50:16
%S A216703 1,42,1911,89180,4213755,200574738,9594158301,460519598448,
%T A216703 22162505675310,1068725273676060,51619430718553698,
%U A216703 2496503376570051576,120872371815599997138,5857661095679076784380,284096563140435224042430,13788153197749122873525936
%N A216703 a(n) = Product_{k=1..n} (49 - 7/k).
%C A216703 This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).
%F A216703 From _Seiichi Manyama_, Jul 17 2025: (Start)
%F A216703 G.f.: 1/(1 - 49*x)^(6/7).
%F A216703 a(n) = (-49)^n * binomial(-6/7,n).
%F A216703 a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+6). (End)
%F A216703 From _Amiram Eldar_, Aug 17 2025: (Start)
%F A216703 a(n) = 49^n * Gamma(n+6/7) / (Gamma(6/7) * Gamma(n+1)).
%F A216703 a(n) ~ c * 49^n / n^(1/7), where c = 1/Gamma(6/7) = 1/A220607 = 0.904349... . (End)
%p A216703 seq(product(49-7/k, k=1.. n), n=0..20);
%p A216703 seq((7^n/n!)*product(7*k+6, k=0.. n-1), n=0..20);
%t A216703 Table[49^n * Pochhammer[6/7, n] / n!, {n, 0, 15}] (* _Amiram Eldar_, Aug 17 2025 *)
%Y A216703 Cf. A004988, A004994, A049382, A216702, A220607.
%Y A216703 Cf. A034835, A386271, A386272, A386273, A386274.
%K A216703 nonn,easy
%O A216703 0,2
%A A216703 _Michel Lagneau_, Sep 16 2012