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A111812 Column 3 of triangle A098539, which shifts columns left and up under matrix square. 0
1, 8, 72, 888, 16392, 479736, 23196168, 1909718520, 273790460424, 69532461669880, 31699923943776776, 26220200137673186808, 39689067731528646091272, 110732781183212424923225592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

G.f.: A(x) = 1 + Sum_{n>=1} 8^n/n!*Product_{j=0..n-1} L(2^j*x) where L(x) = e.g.f. of A111811 (column 0 of matrix log of A098539) satisfies: x = L(x) - L(x)*L(2*x)/2! + L(x)*L(2*x)*L(2^2*x)/3! - L(x)*L(2*x)*L(2^2*x)*L(2^3*x)/4! + ...

EXAMPLE

A(x) = 1 + 8*x + 72*x^2 + 888*x^3 + 16392*x^4 + 479736*x^5 +...

PROG

(PARI) {a(n, q=2)=local(A=Mat(1), B); if(n<0, 0, for(m=1, n+4, 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]=(A^q)[i-1, 1], B[i, j]=(A^q)[i-1, j-1])); )); A=B); return(A[n+4, 4]))}

CROSSREFS

Cf. A098539, A111811.

Sequence in context: A013992 A279156 A129103 * A138433 A242597 A241032

Adjacent sequences:  A111809 A111810 A111811 * A111813 A111814 A111815

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 22 2005

STATUS

approved

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Last modified December 4 13:03 EST 2021. Contains 349526 sequences. (Running on oeis4.)