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A093768 Positive first differences of the rows of triangle A088459, which enumerates symmetric Dyck paths. 5
1, 1, 1, 1, 2, 3, 1, 3, 8, 6, 1, 4, 15, 20, 20, 1, 5, 24, 45, 75, 50, 1, 6, 35, 84, 189, 210, 175, 1, 7, 48, 140, 392, 588, 784, 490, 1, 8, 63, 216, 720, 1344, 2352, 2352, 1764, 1, 9, 80, 315, 1215, 2700, 5760, 7560, 8820, 5292, 1, 10, 99, 440, 1925, 4950, 12375, 19800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Suggested by Bozydar Dubalski (slawb(AT)atr.bydgoszcz.pl). Related to walks on a square lattice: main diagonal forms A005558, secondary diagonals form A005559, A005560, A005561, A005562, A005563.

LINKS

Table of n, a(n) for n=0..62.

FORMULA

T(n, k) = C(n+1, ceil(k/2))*C(n, floor(k/2)) - C(n+1, ceil((k-1)/2))*C(n, floor((k-1)/2)) for n>=k>=0.

PROG

(PARI) {T(n, k) =binomial(n+1, ceil(k/2))*binomial(n, floor(k/2)) -binomial(n+1, ceil((k-1)/2))*binomial(n, floor((k-1)/2))}

CROSSREFS

Cf. A088459, A005558-A005563.

Sequence in context: A100324 A121424 A214978 * A209419 A119011 A130477

Adjacent sequences:  A093765 A093766 A093767 * A093769 A093770 A093771

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Apr 16 2004

STATUS

approved

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Last modified November 26 12:21 EST 2014. Contains 250065 sequences.