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A111976 Column 0 of triangle A111975, which shifts columns left and up under matrix square. 2
1, 1, 1, 4, 16, 96, 896, 13568, 345088, 15112192, 1159913472, 158164664320, 38737429987328, 17197276791701504, 13946909814794223616, 20801835304287183306752, 57394078732651064041930752 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
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).
EXAMPLE
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 +-...
PROG
(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]))}
CROSSREFS
Cf. A111975 (triangle), A111979.
Sequence in context: A293143 A032184 A130683 * A236772 A209299 A091040
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 25 2005
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)