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 A167540 #2 Mar 30 2012 18:37:20
%S A167540 1,4,36,432,6504,118272,2525824,62011648,1721422656,53324108032,
%T A167540 1823657963776,68252530738176,2774853481548288,121780933815238656,
%U A167540 5738394351838543872,288958047466769973248,15485497781445500923904
%N A167540 G.f.: Sum_{n>=0} A155585(2n+1)*log(1-2x)^n/n!, where (1-2*x)^2/(1-2*x+2*x^2) = Sum_{n>=0} A155585(n)*log(1-2x)^n/n!.
%C A167540 Note that A155585(n) = 2^n E_{n}(1) where E_{n}(x) are the Euler polynomials; e.g.f. of A155585 is exp(x)/cosh(x).
%C A167540 CONJECTURE: For integers m>0, b>=0, Sum_{n>=0} L(m*n+b) * log(1+x)^n/n! is an integer series whenever Sum_{n>=0} L(n)*log(1+x)^n/n! is an integer series.
%e A167540 G.f.: A(x) = 1 + 4*x + 36*x^2 + 432*x^3 + 6504*x^4 + 118272*x^5 +...
%e A167540 Illustrate the g.f.:
%e A167540 A(x) = 1 - 2*log(1-2*x) + 16*log(1-2*x)^2/2! - 272*log(1-2*x)^3/3! + 7936*log(1-2*x)^4/4! - 353792*log(1-2*x)^5/5! +...+ A155585(2n+1)*log(1-2x)^n/n! +...
%e A167540 where:
%e A167540 (1-2*x)^2/(1-2*x+2*x^2) = 1 + log(1-2*x) - 2*log(1-2*x)^3/3! + 16*log(1-2*x)^5/5! - 272*log(1-2*x)^7/7! +...+ A155585(n)*log(1-2x)^n/n! +...
%o A167540 (PARI) {A155585(n)=if(n==0,1,bernfrac(n+1)*(2^(n+1)-1)*2^(n+1)/(n+1))}
%o A167540 {a(n)=polcoeff(sum(k=0,n,A155585(2*k+1)*log(1-2*x +x*O(x^n))^k/k!),n)}
%Y A167540 Cf. A155585, variant: A167532.
%K A167540 nonn
%O A167540 0,2
%A A167540 _Paul D. Hanna_, Nov 06 2009