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.
G.f.: A(x) = 1 + 9*x + 405*x^2 + 121500*x^3 + 247203171*x^4 +...
{a(n)=local(M=matrix(n+2, n+2, r, c, binomial(r*3^(c-2), c-1)), P); P=matrix(n+2, n+2, r, c, binomial((r+1)*3^(c-2), c-1)); (P~*M~^-1)[n+2, 2]}
{a(n)=local(M=matrix(n+2, n+2, r, c, binomial(r*3^(c-2), c-1)), P); P=matrix(n+2, n+2, r, c, binomial((r+1)*3^(c-2), c-1)); sum(k=0,n,(P~*M~^-1)[n+1, k+1])}
G.f.: A(x) = 1 + x + 3*x^2 + 84*x^3 + 17550*x^4 + 25621596*x^5 +... A(x) = 1 + log(1+3*x)/3 + log(1+3^2*x)^2/(3^2*2!) + log(1+3^3*x)^3/(3^3*3!) + log(1+3^4*x)^4/(3^4*4!) +...
Table[Binomial[3^(n-1),n], {n,0,15}] (* Vaclav Kotesovec, Jul 02 2016 *)
a(n)=binomial(3^(n-1), n)
/* G.f. A(x) as Sum of Series: */
{a(n)=polcoeff(sum(k=0, n, (1/3)^k*log(1+3^k*x +x*O(x^n))^k/k!), n)}
G.f.: A(x) = 1 + 2*x + 15*x^2 + 816*x^3 + 316251*x^4 +... A(x) = 1 + 2*log(1+3*x)/3 + 2^2*log(1+3^2*x)^2/(3^2*2!) + 2^3*log(1+3^3*x)^3/(3^3*3!) + 2^4*log(1+3^4*x)^4/(3^4*4!) +...
Table[Binomial[2*3^(n-1),n], {n,0,15}] (* Vaclav Kotesovec, Jul 02 2016 *)
{a(n)=binomial(2*3^(n-1), n)}
/* G.f. A(x) as Sum of Series: */
{a(n)=polcoeff(sum(k=0, n, (2/3)^k*log(1+3^k*x +x*O(x^n))^k/k!), n)}
Comments