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A167772 Riordan array (c(x)/(1+x*c(x)),x*c(x)), c(x) the g.f. of A000108. 4
1, 0, 1, 1, 1, 1, 2, 3, 2, 1, 6, 8, 6, 3, 1, 18, 24, 18, 10, 4, 1, 57, 75, 57, 33, 15, 5, 1, 186, 243, 186, 111, 54, 21, 6, 1, 622, 808, 622, 379, 193, 82, 28, 7, 1, 2120, 2742, 2120, 1312, 690, 311, 118, 36, 8, 1, 7338, 9458, 7338, 4596, 2476, 1164, 474, 163, 45, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Rows sums are A000958.

For n > 0: T(n,0) = A065602(n+1,3), T(n,k) = A065602(n+1,k+1), k = 1..n. - Reinhard Zumkeller, May 15 2014

LINKS

Reinhard Zumkeller, Rows n=0..125 of triangle, flattened

FORMULA

Sum_{0<=k<=n} T(n,k)*2^k = A014300(n); Sum_{0<=k<=n} T(n,k)*2^(n-k) = A064306(n). [Philippe Deléham, Nov 12 2009]

EXAMPLE

Triangle begins : 1 ; 0,1 ; 1,1,1 ; 2,3,2,1 ; 6,8,6,3,1 ; 18,24,18,10,4,1 ; ...

Production matrix begins:

0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1

... - Philippe Deléham, Mar 03 2013

PROG

(Haskell)

import Data.List (genericIndex)

a167772 n k = genericIndex (a167772_row n) k

a167772_row n = genericIndex a167772_tabl n

a167772_tabl = [1] : [0, 1] :

               map (\xs@(_:x:_) -> x : xs) (tail a065602_tabl)

-- Reinhard Zumkeller, May 15 2014

CROSSREFS

Cf. A000957, A000958, A104629, A001558, A001559, A167769.

Diagonals: A000012, A001477, A000217, A166830.

Sequence in context: A286156 A113908 A065369 * A077870 A294408 A062323

Adjacent sequences:  A167769 A167770 A167771 * A167773 A167774 A167775

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Nov 11 2009, corrected Nov 12 2009

STATUS

approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)