A193450 Triangle of a binomial convolution sum related to Jacobsthal numbers.

0, 1, 0, 2, 2, 2, 3, 6, 6, 0, 4, 12, 16, 8, 4, 5, 20, 35, 30, 15, 0, 6, 30, 66, 78, 54, 18, 6, 7, 42, 112, 168, 154, 84, 28, 0, 8, 56, 176, 320, 368, 272, 128, 32, 8, 9, 72, 261, 558, 774, 720, 450, 180, 45, 0, 10, 90, 370, 910, 1480, 1660, 1300, 700, 250, 50, 10

Offset

0,4

Comments

Row sum is A193449(n) = A001045(n+1)*n.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = sum( (-1)^j*n*C(n-j,k-j), j=0..k).

T(n,k) = n*C(n, k)*2F1( (1, -k); -n )(-1).

Example

Triangle starts:
0;
1, 0;
2, 2, 2;
3, 6, 6, 0;
4, 12, 16, 8, 4;
5, 20, 35, 30, 15, 0;
...

Prog

(PARI) T(n, k) = sum(j=0, k, (-1)^j*n*binomial(n-j, k-j)); \\ Michel Marcus, Jun 04 2014

Crossrefs

Cf. A193451.

Sequence in context: A104346 A318238 A341075 * A109906 A104856 A306393

Adjacent sequences: A193447 A193448 A193449 * A193451 A193452 A193453

Keyword

nonn,easy,tabl

Author

Olivier Gérard, Jul 26 2011

Status

approved