A113408 Riordan array (1/(1-x^2-x^4*c(x^4)),x*c(x^2)), c(x) the g.f. of A000108.

1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 3, 0, 1, 0, 6, 0, 4, 0, 1, 3, 0, 12, 0, 5, 0, 1, 0, 12, 0, 20, 0, 6, 0, 1, 6, 0, 30, 0, 30, 0, 7, 0, 1, 0, 30, 0, 60, 0, 42, 0, 8, 0, 1, 10, 0, 90, 0, 105, 0, 56, 0, 9, 0, 1, 0, 60, 0, 210, 0, 168, 0, 72, 0, 10, 0, 1, 20, 0, 210, 0, 420, 0, 252, 0, 90, 0, 11, 0, 1

Offset

0,8

Comments

Row sums are A113409. Diagonal sums are A005773(n+1) with interpolated zeros.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

T(n, k) = C((n+k)/2,k)*C(floor((n-k)/2),floor((n-k)/4))(1+(-1)^(n-k))/2.

Example

Triangle begins
1;
0,1;
1,0,1;
0,2,0,1;
2,0,3,0,1;
0,6,0,4,0,1;
3,0,12,0,5,0,1;

Mathematica

Table[Binomial[(n + k)/2, k]*Binomial[Floor[(n - k)/2], Floor[(n - k)/4]]*(1 + (-1)^(n - k))/2, {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Mar 09 2017 *)

Prog

(PARI) for(n=0, 25, for(k=0, n, print1( binomial((n+k)/2, k) *binomial(floor((n-k)/2), floor((n-k)/4))*(1+(-1)^(n-k))/2, ", "))) \\ G. C. Greubel, Mar 09 2017

Crossrefs

Sequence in context: A330635 A322378 A053121 * A242653 A191530 A321435

Adjacent sequences: A113405 A113406 A113407 * A113409 A113410 A113411

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 28 2005

Status

approved