

A118438


Triangle T, read by rows, equal to the matrix product T = H*C*H, where H is the selfinverse triangle A118433 and C is Pascal's triangle.


3



1, 1, 1, 5, 2, 1, 11, 9, 3, 1, 23, 44, 30, 4, 1, 41, 125, 110, 30, 5, 1, 45, 246, 345, 220, 75, 6, 1, 29, 301, 861, 875, 385, 63, 7, 1, 337, 232, 1260, 2296, 1610, 616, 140, 8, 1, 1199, 3015, 1044, 3612, 5166, 3150, 924, 108, 9, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

The matrix inverse of H*C*H is H*[C^1]*H = A118435, where H^2 = I (identity). The matrix log, log(T) = A118441, is a matrix square root of a triangular matrix with a single diagonal (two rows down from the main diagonal).


LINKS

Table of n, a(n) for n=0..54.


FORMULA

Since T + T^1 = C + C^1, then [T^1](n,k) = (1+(1)^(nk))*C(n,k)  T(n,k) is a formula for the matrix inverse T^1 = A118435.


EXAMPLE

Triangle begins:
1;
1, 1;
5,2, 1;
11,9,3, 1;
23, 44, 30,4, 1;
41, 125, 110,30,5, 1;
45,246,345, 220, 75,6, 1;
29,301,861, 875, 385,63,7, 1;
337,232, 1260,2296,1610, 616, 140,8, 1;
1199,3015,1044,3612,5166, 3150, 924,108,9, 1; ...


PROG

(PARI) {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(r1, c1)*(1)^(r\2 (c1)\2+rc))), C=matrix(n+1, n+1, r, c, if(r>=c, binomial(r1, c1)))); (M*C*M)[n+1, k+1]}


CROSSREFS

Cf. A118439 (column 0), A118440 (row sums), A118435 (matrix inverse), A118441 (matrix log); A118433 (selfinverse H).
Sequence in context: A318328 A011507 A136643 * A336244 A083801 A344557
Adjacent sequences: A118435 A118436 A118437 * A118439 A118440 A118441


KEYWORD

sign,tabl


AUTHOR

Paul D. Hanna, Apr 28 2006


STATUS

approved



