login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A205813 Triangle T(n,k), read by rows, given by (0, 2, 1, 1, 1, 1, 1, 1, 1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 4
1, 0, 1, 0, 2, 1, 0, 6, 4, 1, 0, 20, 16, 6, 1, 0, 70, 64, 30, 8, 1, 0, 252, 256, 140, 48, 10, 1, 0, 924, 1024, 630, 256, 70, 12, 1, 0, 3432, 4096, 2772, 1280, 420, 96, 14, 1, 0, 12870, 16384, 12012, 6144, 2310, 640, 126, 16, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Riordan array (1, x/sqrt(1-4x)). Inverse of Riordan array (1, x*exp(arcsinh(-2x)).

LINKS

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

FORMULA

T(n,n) = 1 = A000012(n); T(n+1,n) = 2n = A005843(n); T(n+2,n) = 2n*(n+2) = A054000(n+1).

Sum_{k=0..n} T(n,k)*x^k = -A081696(n-1), A000007(n), A026671(n-1), A084868(n) for x = -1, 0, 1, 2 respectively.

G.f.: sqrt(1-4x)/(sqrt(1-4x)-y*x).

Sum_{k=0..n} T(n,k)*A090192(k) = A000108(n), A000108 = Catalan numbers.

EXAMPLE

Triangle begins:

  1;

  0,   1;

  0,   2,   1;

  0,   6,   4,   1;

  0,  20,  16,   6,   1;

  0,  70,  64,  30,   8,   1;

  0, 252, 256, 140,  48,  10,   1;

CROSSREFS

Cf. A054335 and columns listed there.

Sequence in context: A011312 A275328 A147720 * A127631 A122538 A090238

Adjacent sequences:  A205810 A205811 A205812 * A205814 A205815 A205816

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 01 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 16:19 EDT 2020. Contains 334852 sequences. (Running on oeis4.)