This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386271 #10 Jul 20 2025 15:33:13
%S A386271 1,14,441,16464,662676,27832392,1201431588,52862989872,2359010923038,
%T A386271 106417603861492,4842000975697886,221851681068339504,
%U A386271 10223664969232645476,473434331652157890504,22014696421825341908436,1027352499685182622393680,48092938891512611510804145
%N A386271 Expansion of 1/(1 - 49*x)^(2/7).
%F A386271 a(n) = (-49)^n * binomial(-2/7,n).
%F A386271 a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+2).
%F A386271 a(n) = 7^n * Product_{k=1..n} (7 - 5/k).
%F A386271 In general, 1/(1 - k^2*x)^(m/k) leads to the D-finite recurrence k*(k*n-k+m)*a(n-1) - n*a(n) = 0. This sequence is case k=7, m=2: (49*n-35)*a(n-1) - n*a(n) = 0. - _Georg Fischer_, Jul 19 2025
%o A386271 (PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-49*x)^(2/7))
%Y A386271 Cf. A020918 (k=2, m=7), A020920 (k=2, m=9), A034835 (k=7, m=1), A034977 (k=8, m=1), A035024 (k=9, m=1), A216702 (k=4, m=3), A216703 (k=7, m=6), A354019 (k=6, m=1), this sequence (k=7, m=2), A386272 (k=7, m=3), A386273 (k=7, m=4), A386274 (k=7, m=5).
%K A386271 nonn,easy
%O A386271 0,2
%A A386271 _Seiichi Manyama_, Jul 17 2025