%I #7 Aug 09 2015 15:39:35

%S 1,1,2,3,1,2,5,8,14,1,2,5,10,18,30,49,1,2,5,10,20,34,59,94,149,1,2,5,

%T 10,20,36,63,104,169,264,405,1,2,5,10,20,36,65,108,179,284,445,676,

%U 1017,1,2,5,10,20,36,65,110,183,294,465,716,1089,1622,2387,1,2,5,10,20,36,65

%N The number 1 followed by 2*k+1 terms from column k of table A115994.

%e Column two of table A115994 begins 1 2 5 8 14 20 30 ... A006918

%e so row three of A117488 is 1 2 5 8 14.

%e Triangle starts

%e 1

%e 1 2 3

%e 1 2 5 8 14

%e 1 2 5 10 18 30 49

%e 1 2 5 10 20 34 59 94 149

%e 1 2 5 10 20 36 63 104 169 264 405

%e 1 2 5 10 20 36 65 108 179 284 445 676 1017

%e 1 2 5 10 20 36 65 110 183 294 465 716 1089 1622 2387

%p A026820 := proc(n,k) if k > n then combinat[numbpart](n,n) ; else combinat[numbpart](n,k) ; fi ; end: A115994 := proc(n,k) local i ; add(A026820(i,k)*A026820(n-k^2-i,k),i=0..n-k^2) ; end: A117488 := proc(n,k) if k >= 2*n then 0 ; else if n = 1 then 1; else A115994(k+n^2-2*n,n-1) ; fi ; fi ; end: for n from 1 to 10 do for k from 1 to 2*n-1 do printf("%d ",A117488(n,k)) ; od ; od ; # _R. J. Mathar_, Feb 22 2007

%Y Cf. A006918, A115994, A117489.

%K tabf,nonn

%O 1,3

%A _Alford Arnold_, Mar 22 2006

%E More terms from _R. J. Mathar_, Feb 22 2007