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A339350 Triangle read by rows. T(n,k) = Sum_{j=0..k} binomial(k-j+2, 2)*T(n-1, j), for n>=0, 0<=k<=n, with T(0,0)=1 and T(n,n)=0 for n>0. 0
1, 1, 0, 1, 3, 0, 1, 6, 15, 0, 1, 9, 39, 91, 0, 1, 12, 72, 272, 612, 0, 1, 15, 114, 570, 1995, 4389, 0, 1, 18, 165, 1012, 4554, 15180, 32890, 0, 1, 21, 225, 1625, 8775, 36855, 118755, 254475, 0, 1, 24, 294, 2436, 15225, 75516, 302064, 949344, 2017356, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

Francesca Aicardi, Catalan triangle and tied arc diagrams, arXiv:2011.14628 [math.CO], 2020.

EXAMPLE

Triangle begins:

  1;

  1,  0;

  1,  3,  0;

  1,  6, 15,   0;

  1,  9, 39,  91,   0;

  1, 12, 72, 272, 612, 0;

  ...

PROG

(PARI) T(n, k) = if ((n==0) && (k==0), 1, if (n<=k, 0, sum(j=0, k, binomial(k-j+2, 2)*T(n-1, j))));

CROSSREFS

Cf. subdiagonals: A006632, A006633, A006634, A006635.

Sequence in context: A100485 A143397 A341856 * A244118 A273155 A208345

Adjacent sequences:  A339347 A339348 A339349 * A339351 A339352 A339353

KEYWORD

nonn,tabl

AUTHOR

Michel Marcus, Dec 01 2020

STATUS

approved

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Last modified December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)