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 A300614 #9 Mar 10 2018 07:57:57
%S A300614 1,1,33,118195,3419881993,412433022394701,152749066271797582081,
%T A300614 143430189975946314906194983,297572051428536567500380512047505,
%U A300614 1228369468294423956894049108209998483353,9295358239339907973775754707697954813272247041,120806095217585335844962641542342569940874366294995451
%N A300614 E.g.f. A(x) satisfies: [x^n] A(x)^(n^5) = n^5 * [x^(n-1)] A(x)^(n^5) for n>=1.
%C A300614 Compare e.g.f. to: [x^n] exp(x)^(n^5) = n^4 * [x^(n-1)] exp(x)^(n^5) for n>=1.
%H A300614 Paul D. Hanna, <a href="/A300614/b300614.txt">Table of n, a(n) for n = 0..150</a>
%F A300614 E.g.f. A(x) satisfies: log(A(x)) = Sum_{n>=1} A300615(n)*x^n, a power series in x with integer coefficients.
%e A300614 E.g.f.: A(x) = 1 + x + 33*x^2/2! + 118195*x^3/3! + 3419881993*x^4/4! + 412433022394701*x^5/5! + 152749066271797582081*x^6/6! + 143430189975946314906194983*x^7/7! + ...
%e A300614 ILLUSTRATION OF DEFINITION.
%e A300614 The table of coefficients of x^n in A(x)^(n^5) begins:
%e A300614 n=1: [(1), (1), 33/2, 118195/6, 3419881993/24, 137477674131567/40, ...];
%e A300614 n=2: [1, (32), (1024), 1955104/3, 13739402240/3, 1651861749195104/15, ...];
%e A300614 n=3: [1, 243, (66825/2), (16238475/2), 288411062643/8, 33749327928610701/40, ...];
%e A300614 n=4: [1, 1024, 540672, (647668736/3), (663212785664/3), 18460138990560256/5, ...];
%e A300614 n=5: [1, 3125, 9865625/2, 31824134375/6, (116555654565625/24), (364236420517578125/24), ...];
%e A300614 n=6: [1, 7776, 30357504, 79484677920, 158407197944832, (1433574291388125024/5), (11147473689834060186624/5), ...]; ...
%e A300614 in which the coefficients in parenthesis are related by
%e A300614 1 = 1*1; 1024 = 2^5*32; 16238475/2 = 3^5*66825/2; 663212785664/3 = 4^5*647668736/3; ...
%e A300614 illustrating that: [x^n] A(x)^(n^5) = n^5 * [x^(n-1)] A(x)^(n^5).
%e A300614 LOGARITHMIC PROPERTY.
%e A300614 The logarithm of the e.g.f. is the integer series:
%e A300614 log(A(x)) = x + 16*x^2 + 19683*x^3 + 142475264*x^4 + 3436799053125*x^5 + 212148041589128016*x^6 + 28458158819417861315152*x^7 + 7380230750280159370894934016*x^8 + ... + A300615(n)*x^n + ...
%o A300614 (PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^5)); A[#A] = ((#A-1)^5*V[#A-1] - V[#A])/(#A-1)^5 ); n!*A[n+1]}
%o A300614 for(n=0, 20, print1(a(n), ", "))
%Y A300614 Cf. A182962, A296170, A300590, A300592, A300594, A300596, A300615.
%K A300614 nonn
%O A300614 0,3
%A A300614 _Paul D. Hanna_, Mar 10 2018