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 A235128 #19 Jun 24 2025 04:13:27
%S A235128 1,1,8,71,1072,20161,476288,13315751,432387712,15959926081,
%T A235128 660372282368,30265936565831,1522069164439552,83327826089289601,
%U A235128 4933286107483701248,314052936209639958311,21392225375507849838592,1552501782546292090638721,119588747474281844162428928
%N A235128 Expansion of e.g.f. 1/(1 - sin(7*x))^(1/7).
%C A235128 Generally, for e.g.f. 1/(1-sin(p*x))^(1/p) we have a(n) ~ n! * 2^(n+3/p) * p^n / (Gamma(2/p) * n^(1-2/p) * Pi^(n+2/p)).
%F A235128 a(n) ~ n! * 2^(n+3/7) * 7^n / (Gamma(2/7) * n^(5/7) * Pi^(n+2/7)).
%F A235128 a(n) = Sum_{k=0..n} A045754(k) * (7*i)^(n-k) * A136630(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Jun 24 2025
%t A235128 CoefficientList[Series[1/(1-Sin[7*x])^(1/7), {x, 0, 20}], x] * Range[0, 20]!
%o A235128 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A235128 a045754(n) = prod(k=0, n-1, 7*k+1);
%o A235128 a(n) = sum(k=0, n, a045754(k)*(7*I)^(n-k)*a136630(n, k)); \\ _Seiichi Manyama_, Jun 24 2025
%Y A235128 Cf. A001586 (p=2), A007788 (p=3), A144015 (p=4), A230134 (p=5), A227544 (p=6), A230114 (p=8).
%Y A235128 Cf. A045754, A136630.
%K A235128 nonn,easy
%O A235128 0,3
%A A235128 _Vaclav Kotesovec_, Jan 03 2014