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A257566 Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} P(n,j)*T(n-j,k-1) if k>0 else 0^n where P(n,j) is the number of j-partitions of n; for n>=0 and 0<=k<=n. 1

%I #8 Apr 30 2015 21:12:47

%S 1,0,1,0,2,1,0,3,4,1,0,5,13,7,1,0,7,30,30,10,1,0,11,76,119,65,14,1,0,

%T 15,152,357,306,113,18,1,0,22,330,1119,1375,746,193,23,1,0,30,633,

%U 2973,5059,3888,1497,295,28,1,0,42,1245,8036,18605,19423,10298,2930,447,34,1

%N Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} P(n,j)*T(n-j,k-1) if k>0 else 0^n where P(n,j) is the number of j-partitions of n; for n>=0 and 0<=k<=n.

%F T(n,1) = A000041(n) for n>=1.

%F T(n,n-1) = A014616(n-1) for n>=2.

%e 1;

%e 0, 1;

%e 0, 2, 1;

%e 0, 3, 4, 1;

%e 0, 5, 13, 7, 1;

%e 0, 7, 30, 30, 10, 1;

%e 0, 11, 76, 119, 65, 14, 1;

%p T := proc(n,k) option remember; `if`(k=0, 0^n,

%p add(combinat:-numbpart(n,j)*T(n-j, k-1), j=0..n-k+1)) end:

%p for n from 0 to 12 do seq(T(n, k), k=0..n) od;

%Y Cf. A000041, A014616.

%K nonn,tabl,easy

%O 0,5

%A _Peter Luschny_, Apr 30 2015

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)