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A237619 Riordan array (1/(1+x*c(x)), x*c(x)) where c(x) is the g.f. of Catalan numbers (A000108). 1
1, -1, 1, 0, 0, 1, -1, 1, 1, 1, -2, 2, 3, 2, 1, -6, 6, 8, 6, 3, 1, -18, 18, 24, 18, 10, 4, 1, -57, 57, 75, 57, 33, 15, 5, 1, -186, 186, 243, 186, 111, 54, 21, 6, 1, -622, 622, 808, 622, 379, 193, 82, 28, 7, 1, -2120, 2120, 2742, 2120, 1312, 690, 311, 118, 36 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

T(n,0) = A126983(n).

T(n+1,1) = A000957(n+1).

T(n+2,2) = A000958(n+1).

T(n+3,3) = A104629(n) = A000957(n+3).

T(n+4,4) = A001558(n).

T(n+5,5) = A001559(n).

LINKS

Table of n, a(n) for n=0..63.

FORMULA

Sum_{k=0..n} T(n,k)*x^k = A126983(n), A000957(n+1), A026641(n) for x = 0, 1, 2 respectively.

T(n+1,k+1) = A167772(n,k).

EXAMPLE

Triangle begins:

1;

-1, 1;

0, 0, 1;

-1, 1, 1, 1;

-2, 2, 3, 2, 1;

-6, 6, 8, 6, 3, 1;

-18, 18, 24, 18, 10, 4, 1;

-57, 57, 75, 57, 33, 15, 5, 1;

...

Production matrix begins:

-1...1

-1...1...1

-1...1...1...1

-1...1...1...1...1

-1...1...1...1...1...1

-1...1...1...1...1...1...1

-1...1...1...1...1...1...1...1

-1...1...1...1...1...1...1...1...1

...

CROSSREFS

Cf. Diagonals: A000012, A023443, A000217, A166830.

Cf. A167772

Sequence in context: A185694 A305294 A097510 * A156747 A318958 A194827

Adjacent sequences:  A237616 A237617 A237618 * A237620 A237621 A237622

KEYWORD

sign,tabl

AUTHOR

Philippe Deléham, Feb 10 2014

STATUS

approved

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