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 A359918 #11 Mar 21 2024 04:54:39
%S A359918 1,2,21,304,6985,205056,7607509,337188608,17495079921,1038495001600,
%T A359918 69496455755221,5176052539987968,424783071501394489,
%U A359918 38087843235679268864,3704990294840345047125,388631778963216211050496,43729459820175064700435041,5254332451028464517449777152
%N A359918 a(n) = coefficient of x^n*y^(n+1)/n! in (1/2) * log( Sum_{n>=0} (n^2 + n*y + 2*y^2)^n * x^n/n! ).
%H A359918 Paul D. Hanna, <a href="/A359918/b359918.txt">Table of n, a(n) for n = 1..200</a>
%F A359918 a(n) ~ c * d^n * n! / n^(5/2), where d = 7.68892218919697462312... and c = 0.1314019396717313039... - _Vaclav Kotesovec_, Mar 21 2024
%e A359918 E.g.f.: A(x) = x + 2*x^2/2! + 21*x^3/3! + 304*x^4/4! + 6985*x^5/5! + 205056*x^6/6! + 7607509*x^7/7! + 337188608*x^8/8! + 17495079921*x^9/9! + 1038495001600*x^10/10! + ...
%e A359918 Exponentiation yields the e.g.f. of A359917:
%e A359918 exp(A(x)) = 1 + x + 3*x^2/2! + 28*x^3/3! + 413*x^4/4! + 9216*x^5/5! + 268327*x^6/6! + 9831424*x^7/7! + 432251577*x^8/8! +...+ A359917(n)*x^n/n! + ...
%e A359918 which equals
%e A359918 lim_{N->oo} [ Sum_{n>=0} (N^2 + N*n + 2*n^2)^n * (x/N)^n/n! ]^(1/N).
%e A359918 RELATED SEQUENCES.
%e A359918 a(n) is divisible by n where a(n)/n begins:
%e A359918 [1, 1, 7, 76, 1397, 34176, 1086787, 42148576, 1943897769, 103849500160, ...].
%o A359918 (PARI) {a(n) = (1/2) * n! * polcoeff( polcoeff( log( sum(m=0, n+1, (m^2 + m*y + 2*y^2)^m *x^m/m! ) +x*O(x^n) ), n, x), n+1, y)}
%o A359918 for(n=1, 30, print1(a(n), ", "))
%Y A359918 Cf. A359917, A359926, A359928, A319834, A318634.
%K A359918 nonn
%O A359918 1,2
%A A359918 _Paul D. Hanna_, Jan 21 2023