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A116395 Riordan array (1/sqrt(1-4x), (1/sqrt(1-4x)-1)/2). 7
1, 2, 1, 6, 5, 1, 20, 22, 8, 1, 70, 93, 47, 11, 1, 252, 386, 244, 81, 14, 1, 924, 1586, 1186, 500, 124, 17, 1, 3432, 6476, 5536, 2794, 888, 176, 20, 1, 12870, 26333, 25147, 14649, 5615, 1435, 237, 23, 1, 48620, 106762, 112028, 73489, 32714, 10135, 2168, 307, 26, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A007854. Diagonal sums are A116396.

Triangle T(n,k), 0<=k<=n, read by rows given by [2,1,1,1,1,1,1,...] DELTA [1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - Philippe Deléham, Jun 05 2007

Inverse of Riordan array (1/(1+2x), x(1+x)/(1+2x)^2) (see A123876). - Philippe Deléham, Oct 25 2007

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Number triangle T(n,k)=(4^n/2^k)*sum{j=0..k, C(k,j)C(n+(j-1)/2,n)(-1)^(k-j)}

Sum_{k, 0<=k<=n}(-1)^k*T(n,k)=A000108(n), Catalan numbers . - Philippe Deléham, Nov 07 2006

T(n,k)=Sum_{j, j>=0}A039599(n,j)*binomial(j,k). - Philippe Deléham, Mar 30 2007

Sum_{k, 0<=k<=n}T(n,k)*x^k = A127053(n), A126985(n), A127016(n), A127017(n), A126987(n), A126986(n), A126982(n), A126984(n), A126983(n), A000007(n), A000108(n), A000984(n), A007854(n), A076035(n), A076036(n), A127628(n), A126694(n), A115970(n) for x = -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 respectively . - Philippe Deléham, Oct 25 2007

EXAMPLE

Triangle begins

1,

2, 1,

6, 5, 1,

20, 22, 8, 1,

70, 93, 47, 11, 1,

252, 386, 244, 81, 14, 1

CROSSREFS

Sequence in context: A193723 A260914 A159965 * A159924 A133367 A179456

Adjacent sequences:  A116392 A116393 A116394 * A116396 A116397 A116398

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Feb 12 2006

STATUS

approved

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Last modified December 12 20:04 EST 2017. Contains 295954 sequences.