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 A187740 #10 Jun 18 2025 11:32:14
%S A187740 1,6,85,1650,40500,1200000,41625000,1653750000,74025000000,
%T A187740 3685500000000,201993750000000,12084187500000000,783523125000000000,
%U A187740 54729675000000000000,4097124281250000000000,327237848437500000000000,27775310062500000000000000,2496585341250000000000000000
%N A187740 G.f.: Sum_{n>=0} (5*n+1)^n * x^n / (1 + (5*n+1)*x)^n.
%F A187740 a(n) = (5*n+7) * 5^(n-1) * n!/2 for n>0 with a(0)=1.
%F A187740 E.g.f.: (2 - 8*x + 15*x^2) / (2*(1-5*x)^2).
%e A187740 G.f.: A(x) = 1 + 6*x + 85*x^2 + 1650*x^3 + 40500*x^4 + 1200000*x^5 +...
%e A187740 where
%e A187740 A(x) = 1 + 6*x/(1+6*x) + 11^2*x^2/(1+11*x)^2 + 16^3*x^3/(1+16*x)^3 + 21^4*x^4/(1+21*x)^4 + 26^5*x^5/(1+26*x)^5 +...
%o A187740 (PARI) {a(n)=polcoeff(sum(m=0, n, ((5*m+1)*x)^m/(1+(5*m+1)*x +x*O(x^n))^m), n)}
%o A187740 for(n=0, 20, print1(a(n), ", "))
%Y A187740 Cf. A187735, A014479, A187738, A187739, A221160, A221161.
%K A187740 nonn
%O A187740 0,2
%A A187740 _Paul D. Hanna_, Jan 03 2013