A134051 Column 0 of matrix square of triangle A134049; a(n) = [A134049^2](n,0) = A134049(n+1,1)/2^n.

1, 2, 10, 134, 5296, 654070, 263360560, 357003975476, 1669795729960304, 27463303283181254246, 1611997717693371814854368, 341658984940005114542280763676, 263970944698309599873282861747395376, 749286382285580603530480750573407791776124, 7865298802379026632132665433693770690173266977568, 307033171145749412684239046186235780900756052952468535976, 44787318088048191911792372704769709799574702261206913048329680992

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+1, 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+2, 2]/2^n}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A134049; columns: A134050, A134052, A134053; A134054 (row sums).

Sequence in context: A355463 A336537 A118183 * A075199 A134981 A087417

Adjacent sequences: A134048 A134049 A134050 * A134052 A134053 A134054

Keyword

nonn

Author

Paul D. Hanna, Oct 04 2007

Status

approved