This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. Helms, Number array not found in OEIS, SeqFan list Aug 27 2011 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: A232149 A282422 A282685 * A060487 A285020 A165781 Adjacent sequences:  A194580 A194581 A194582 * A194584 A194585 A194586 KEYWORD nonn,tabl AUTHOR R. J. Mathar, Aug 29 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.