A134052 Column 0 of matrix 4th power of triangle A134049; a(n) = [A134049^4](n,0) = A134049(n+2,2)/4^n.

1, 4, 36, 876, 63520, 14568940, 11015752544, 28298819937896, 252647456547947232, 7975964313047992544460, 902538504812752048885181888, 370060584941821136890734642254392, 554686213433000991860635347227024504416, 3061850209996287672654225041045426728192508664, 62630012990169232252394969915444571881064532934837824, 4772629734773204290203117007836601388039453077250181639664976, 1361188462171480354335535757250707673963106696295682082795368090890432

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+2, 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+3, 3]/4^n}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A134049; columns: A134050, A134051, A134053; A134054 (row sums).

Sequence in context: A126152 A353996 A009446 * A127901 A061742 A136469

Adjacent sequences: A134049 A134050 A134051 * A134053 A134054 A134055

Keyword

nonn

Author

Paul D. Hanna, Oct 04 2007

Status

approved