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A113408 Riordan array (1/(1-x^2-x^4*c(x^4)),x*c(x^2)), c(x) the g.f. of A000108. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A281666 A049803 A053121 * A242653 A191530 A173863

Adjacent sequences:  A113405 A113406 A113407 * A113409 A113410 A113411

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 28 2005

STATUS

approved

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)