cp's OEIS Frontend

A090824 Triangle read by rows: T(n,k) = number of partitions of binomial(n,k) into parts greater than k and not greater than n, 0<=k<=n.

%I A090824 #16 Oct 15 2012 22:15:17
%S A090824 0,1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,2,2,1,1,0,1,4,7,4,1,1,0,1,4,20,19,5,
%T A090824 1,1,0,1,7,67,159,57,8,1,1,0,1,8,238,1607,1163,157,9,1,1,0,1,12,868,
%U A090824 20478,37251,7546,387,13,1,1,0,1,14,3311,312511,1749868,688733,41377,895,16,1,1,0
%N A090824 Triangle read by rows: T(n,k) = number of partitions of binomial(n,k) into parts greater than k and not greater than n, 0<=k<=n.
%C A090824 n>0: T(n,0) = 1, T(n,1) = A002865(n);
%C A090824 T(n,n-2) = 1 for n>1; T(n,n-1) = 1 for n>0; T(n,n) = 0.
%H A090824 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%e A090824 T(6,2) = #{partitions of binomial(6,2)=15 into parts i with 2<i<=6}
%e A090824 = #{6+6+3, 6+5+4, 6+3+3+3, 5+5+5, 5+4+3+3, 4+4+4+3, 3+3+3+3+3} = 7;
%e A090824 T(6,3) = #{partitions of binomial(6,3)=20 into parts i with 3<i<=6}
%e A090824 = #{6+6+4+4, 6+5+5+4, 5+5+5+5, 4+4+4++4+4} = 4.
%o A090824 (Haskell)
%o A090824 a090824 n k = a090824_tabl !! n !! k
%o A090824 a090824_row n = a090824_tabl !! n
%o A090824 a090824_tabl = zipWith (zipWith p)
%o A090824    (map (\x -> map (`enumFromTo` x) [1..x+1]) [0..]) a007318_tabl
%o A090824    where p _          0 = 1
%o A090824          p []         _ = 0
%o A090824          p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o A090824 -- _Reinhard Zumkeller_, Oct 10 2012
%Y A090824 Cf. A000041, A007318.
%K A090824 nonn,tabl
%O A090824 0,12
%A A090824 _Reinhard Zumkeller_, Feb 16 2004
%E A090824 Offset and example corrected by _Reinhard Zumkeller_, Oct 10 2012