A271776 Triangle T(n,m) = Sum_{k=0..m} (-1)^(m-k)*binomial(m,k)*binomial(n-m+k-1,m-1)*binomial(2*n-3*m+k-1,n-m), T(n,n)=1.

1, 1, 1, 2, 2, 1, 6, 5, 3, 1, 20, 18, 9, 4, 1, 70, 70, 37, 14, 5, 1, 252, 280, 162, 64, 20, 6, 1, 924, 1134, 720, 309, 100, 27, 7, 1, 3432, 4620, 3206, 1500, 525, 146, 35, 8, 1, 12870, 18876, 14238, 7238, 2751, 825, 203, 44, 9, 1, 48620, 77220, 62964, 34608, 14240, 4626, 1225, 272, 54, 10, 1

Offset

1,4

Links

Table of n, a(n) for n=1..66.

Example

1;
1,1;
2,2,1;
6,5,3,1;
20,18,9,4,1;
70,70,37,14,5,1;
252,280,162,64,20,6,1;

Mathematica

Table[If[m == n, 1, Sum[(-1)^(m - k) Binomial[m, k] Binomial[n - m + k - 1, m - 1] Binomial[2 n - 3 m + k - 1, n - m], {k, 0, m}]], {n, 11}, {m, n}] (* Michael De Vlieger, Apr 14 2016 *)

Crossrefs

Cf. A000984.

Sequence in context: A174302 A108074 A189175 * A171486 A127743 A125278

Adjacent sequences: A271773 A271774 A271775 * A271777 A271778 A271779

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 14 2016

Status

approved