login
A194583
Triangle T(n,k) with T(n,0)=1 and T(n,k) = (2^(n+1)-2^k)*T(n,k-1) + T(n+1,k-1) otherwise.
1
1, 1, 3, 1, 7, 43, 1, 15, 211, 2619, 1, 31, 931, 26251, 654811, 1, 63, 3907, 234795, 13255291, 662827803, 1, 127, 16003, 1985131, 238658491, 26961325147, 2699483026843, 1, 255, 64771, 16323819, 4050110011, 973958217435, 220115609012251, 44102911693372059, 1, 511, 260611, 132393451, 66733574971, 33115631264731, 15928113739803931, 7200501591899676571, 2886238576935227688091
OFFSET
0,3
LINKS
FORMULA
T(n,1) = A000225(n+1).
T(n,2) = (2^(n+1)-4)*(2^(n+1)-1) + 2^(n+2) - 1.
T(n,k) = -Sum_{j=1..k+1} A158474(k+1,j)*T(n-j,k) assuming the symmetric extension T(n,k) = T(k,n).
EXAMPLE
The triangle starts in row n=0 as
1;
1, 3;
1, 7, 43;
1, 15, 211, 2619;
1, 31, 931, 26251, 654811;
MAPLE
A194583 := proc(n, k) option remember; if n=0 or k=0 then 1; elif k> n then
return procname(k, n); else (2^(n+1)-2^k)*procname(n, k-1)+procname(n+1, k-1) ; end if;
end proc:
MATHEMATICA
t[_, 0] = 1; t[n_, k_] := t[n, k] = (2^(n+1)-2^k)*t[n, k-1]+t[n+1, k-1]; Table[t[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 10 2014 *)
CROSSREFS
Sequence in context: A348115 A282422 A282685 * A346784 A060487 A285020
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Aug 29 2011
STATUS
approved