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A185812 Riordan array ( 1/(1-x), x*A005043(x) ). 3
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 6, 5, 4, 1, 1, 1, 12, 12, 7, 5, 1, 1, 1, 27, 26, 19, 9, 6, 1, 1, 1, 63, 63, 43, 27, 11, 7, 1, 1, 1, 154, 153, 110, 63, 36, 13, 8, 1, 1, 1, 386, 386, 275, 169, 86, 46, 15, 9, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

FORMULA

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

R(n,0)=1.

EXAMPLE

Array begins:

  1;

  1,  1;

  1,  1,  1;

  1,  2,  1,  1;

  1,  3,  3,  1,  1;

  1,  6,  5,  4,  1,  1;

  1, 12, 12,  7,  5,  1,  1;

  1, 27, 26, 19,  9,  6,  1,  1;

MAPLE

A185812 := proc(n, k) if n = k  or k =0 then 1; else k*add(1/(n-i)*add(binomial(2*j-k-1, j-1) *(-1)^(n-j-i) *binomial(n-i, j), j=k..n-i), i=0..n-k) ; end if; end proc:

seq(seq(A185812(n, k), k=0..n), n=0..15) ; # R. J. Mathar, Feb 10 2011

MATHEMATICA

r[n_, k_] := k*Sum[Binomial[2*j - k - 1, j - 1]*(-1)^(n - j - i)*Binomial[n - i, j]/(n - i), {i, 0, n - k}, {j, k, n - i}]; r[n_, 0] = 1; Table[r[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Feb 21 2013 *)

CROSSREFS

Cf. A082395, apparently R(n,1), A097332 (row sums). - R. J. Mathar, Feb 10 2011

Sequence in context: A110541 A331461 A238016 * A152798 A079115 A072906

Adjacent sequences:  A185809 A185810 A185811 * A185813 A185814 A185815

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Feb 05 2011

STATUS

approved

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Last modified July 29 17:26 EDT 2021. Contains 346346 sequences. (Running on oeis4.)