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A185945 Riordan array ( (1/(1-x))^m , x*A000108(x) ), m =4. 3
1, 4, 1, 10, 5, 1, 20, 16, 6, 1, 35, 43, 23, 7, 1, 56, 109, 74, 31, 8, 1, 84, 279, 223, 114, 40, 9, 1, 120, 750, 666, 387, 164, 50, 10, 1, 165, 2148, 2028, 1278, 612, 225, 61, 11, 1, 220, 6529, 6364, 4216, 2188, 910, 298, 73, 12, 1, 286, 20811, 20591, 14062, 7698, 3482, 1294, 384, 86, 13, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

R(n,k,m) = k*Sum_{i=0..n-k} binomial(i+m-1, m-1)*binomial(2*(n-i)-k-1, n-i-1)/(n-i), m=4, k > 0.

R(n,0,4) = binomial(n+3,3) = A000292(n+1).

EXAMPLE

Array begins

    1;

    4,   1;

   10,   5,   1;

   20,  16,   6,   1;

   35,  43,  23,   7,   1;

   56, 109,  74,  31,   8,   1;

   84, 279, 223, 114,  40,   9,   1;

  120, 750, 666, 387, 164,  50,  10,   1;

Production matrix begins:

   4, 1;

  -6, 1, 1;

  10, 1, 1, 1;

  -9, 1, 1, 1, 1;

   7, 1, 1, 1, 1, 1;

  -3, 1, 1, 1, 1, 1, 1;

   1, 1, 1, 1, 1, 1, 1, 1;

   0, 1, 1, 1, 1, 1, 1, 1, 1;

   0, 1, 1, 1, 1, 1, 1, 1, 1, 1;

   0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;

  ... Philippe Deléham, Sep 20 2014

MATHEMATICA

r[n_, k_, m_] := k*Sum[ Binomial[i + m - 1, m - 1]*Binomial[2*(n - i) - k - 1, n - i - 1]/(n - i), {i, 0, n - k}]; r[n_, 0, 4] = Binomial[n + 3, 3]; Table[ r[n, k, 4], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 21 2013 *)

CROSSREFS

Cf. A091491 (m=1), A185943 (m=2), A185944 (m=3).

Cf. A000108, A000292.

Sequence in context: A039806 A030320 A104713 * A186368 A185676 A277583

Adjacent sequences:  A185942 A185943 A185944 * A185946 A185947 A185948

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Feb 07 2011

STATUS

approved

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Last modified July 14 10:07 EDT 2020. Contains 335721 sequences. (Running on oeis4.)