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A144944 Super-Catalan triangle (read by rows) = triangular array associated with little Schroeder numbers (read by rows): T(0,0)=1, T(p,q)=T(p,q-1) if 0<p=q, T(p,q) = T(p,q-1) + T(p-1,q) + T(p-1,q-1) if -1<p<q and T(p,q)=0 otherwise. 4
1, 1, 1, 1, 3, 3, 1, 5, 11, 11, 1, 7, 23, 45, 45, 1, 9, 39, 107, 197, 197, 1, 11, 59, 205, 509, 903, 903, 1, 13, 83, 347, 1061, 2473, 4279, 4279, 1, 15, 111, 541, 1949, 5483, 12235, 20793, 20793, 1, 17, 143, 795, 3285, 10717, 28435, 61463, 103049, 103049 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757, 2015. See Fig. 8

EXAMPLE

First few rows of the triangle:

  1

  1,  1

  1,  3,  3

  1,  5, 11,  11

  1,  7, 23,  45,  45

  1,  9, 39, 107, 197, 197

  1, 11, 59, 205, 509, 903, 903

MATHEMATICA

t[_, 0] = 1; t[p_, p_] := t[p, p] = t[p, p-1]; t[p_, q_] := t[p, q] = t[p, q-1] + t[p-1, q] + t[p-1, q-1]; Flatten[ Table[ t[p, q], {p, 0, 6}, {q, 0, p}]] (* Jean-François Alcover, Dec 19 2011 *)

PROG

(Haskell)

a144944 n k = a144944_tabl !! n !! k

a144944_row n = a144944_tabl !! n

a144944_tabl = iterate f [1] where

   f us = vs ++ [last vs] where

     vs = scanl1 (+) $ zipWith (+) us $ [0] ++ us

-- Reinhard Zumkeller, May 11 2013

CROSSREFS

Super-Catalan numbers or little Schroeder numbers (cf. A001003) appear on the diagonal.

Generalizes the Catalan triangle (A009766) and hence the ballot Numbers.

Cf. A033877 for a similar triangle derived from the large Schroeder numbers (A006318).

Cf. A010683 (row sums), A186826 (rows reversed).

Sequence in context: A193823 A071945 A209583 * A137426 A269949 A074456

Adjacent sequences:  A144941 A144942 A144943 * A144945 A144946 A144947

KEYWORD

nice,nonn,tabl

AUTHOR

Johannes Fischer (Fischer(AT)informatik.uni-tuebingen.de), Sep 26 2008

STATUS

approved

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Last modified February 20 19:06 EST 2018. Contains 299382 sequences. (Running on oeis4.)