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A193450 Triangle of a binomial convolution sum related to Jacobsthal numbers. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A156820 A104346 A318238 * A109906 A104856 A306393

Adjacent sequences:  A193447 A193448 A193449 * A193451 A193452 A193453

KEYWORD

nonn,easy,tabl

AUTHOR

Olivier Gérard, Jul 26 2011

STATUS

approved

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Last modified February 17 17:27 EST 2019. Contains 320222 sequences. (Running on oeis4.)