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Matrix inverse of triangle A136501, read by rows.
3

%I #2 Mar 30 2012 18:37:08

%S 1,-1,1,2,-2,1,-7,7,-4,1,44,-44,26,-8,1,-516,516,-308,100,-16,1,11622,

%T -11622,6959,-2296,392,-32,1,-512022,512022,-306888,101754,-17712,

%U 1552,-64,1,44588536,-44588536,26732904,-8877272,1554404,-139104,6176,-128,1

%N Matrix inverse of triangle A136501, read by rows.

%F G.f. for column k: 1 = Sum_{n>=0} T(n+k,k)*x^n*(1+x)^(2^(n+k)).

%e Triangle begins:

%e 1;

%e -1, 1;

%e 2, -2, 1;

%e -7, 7, -4, 1;

%e 44, -44, 26, -8, 1;

%e -516, 516, -308, 100, -16, 1;

%e 11622, -11622, 6959, -2296, 392, -32, 1;

%e -512022, 512022, -306888, 101754, -17712, 1552, -64, 1;

%e 44588536, -44588536, 26732904, -8877272, 1554404, -139104, 6176, -128, 1;

%o (PARI) {T(n,k)=local(M=matrix(n+1,n+1,r,c,binomial(2^(c-1),r-c)));(M^-1)[n+1,k+1]}

%Y Cf. A107354 (column 0), A136503 (column 2), A136504 (row sums) ; A136501 (matrix inverse).

%K sign,tabl

%O 0,4

%A _Paul D. Hanna_, Jan 01 2008