A134053 Column 0 of matrix 8th power of triangle A134049; a(n) = [A134049^8](n,0) = A134049(n+3,3)/8^n.

1, 8, 136, 6232, 854848, 373259224, 540477342400, 2672052251004112, 46088422295844824512, 2819594595499446574537112, 619804662273405542773923781504, 494669890490702036481614523776214128, 1445689562032160359098054773761542867676352, 15582205179106128515694061249394708070061006521840, 623164384826393004269624677225320058520632702496162024576, 92950754406669433360560292231532867334028809841256765779355298464, 51944751631411703759398930923077536382840396924192243346470672357124333952

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..40

Example

Triangle T=A134049 has the following properties:
(1) [T^(2^m)](n,k) = T(n+m,k+m)/(2^m)^(n-k) for m>=0; and
(2) [T^( 1/2^(n-1) )](n,k) = (2^k)^(n-k) for n>=k>=0.

Prog

(PARI) {a(n)=local(M=Mat(1), L, R); for(i=1, n+3, L=sum(j=1, #M, -(M^0-M)^j/j); M=sum(j=0, #L, (L/2^(#L-1))^j/j!); R=matrix(#M+1, #M+1, r, c, if(r>=c, if(r<=#M, M[r, c], 2^((c-1)*(#M+1-c))))); M=R^(2^(#R-2)) ); M[n+4, 4]/8^n}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A134049; columns: A134050, A134051, A134052; A134054 (row sums).

Sequence in context: A238465 A049211 A024283 * A136472 A145404 A101388

Adjacent sequences: A134050 A134051 A134052 * A134054 A134055 A134056

Keyword

nonn

Author

Paul D. Hanna, Oct 04 2007

Status

approved