0,4

G.f.: A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{j=0..n-1} L(2^j*x) where L(x) satisfies: x-x^2 = Sum_{j>=1}(1-2^j*x)*Prod_{i=0..j-1}L(2^i*x); and L(x) equals the g.f. of column 0 of the matrix log of A111975 (A111979).

G.f. A(x) = 1 + x + x^2 + 4*x^3 + 16*x^4 + 96*x^5 + 896*x^6 +...

= 1 + L(x) + L(x)*L(2*x)/2! + L(x)*L(2*x)*L(2^2*x)/3! +...

where L(x) = x + 16/3!*x^3 + 1536/5!*x^5 - 319488/7!*x^7 +-...

(PARI) {a(n, q=2)=local(A=Mat(1), B); if(n<0, 0, for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=if(i>2, (A^q)[i-1, 2], 1), B[i, j]=(A^q)[i-1, j-1])); )); A=B); return(A[n+1, 1]))}

Cf. A111975 (triangle), A111979.

Sequence in context: A098580 A027745 A032184 this_sequence A130683 A091040 A029985

Adjacent sequences: A111973 A111974 A111975 this_sequence A111977 A111978 A111979

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2005