A187887 Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)).

1, 3, 1, 9, 4, 1, 29, 13, 5, 1, 99, 42, 18, 6, 1, 351, 141, 60, 24, 7, 1, 1275, 492, 201, 84, 31, 8, 1, 4707, 1767, 693, 285, 115, 39, 9, 1, 17577, 6474, 2460, 978, 400, 154, 48, 10, 1, 66197, 24051, 8934, 3438, 1378, 554, 202, 58, 11, 1, 250953, 90248, 32985, 12372, 4816, 1932, 756, 260, 69, 12, 1

Offset

0,2

Comments

Row sums are A082590.

First column is A006134.

Links

Table of n, a(n) for n=0..65.

Formula

a(n,k) = [x^n] 1/((1-x)*sqrt(1-4*x))*(x/(1-x))^k.

Recurrence: a(n+1,k+1) = a(n,k+1) + a(n,k).

a(n,k) = sum(binomial(n-i,k)*binomial(2*i,i),i=0..n).

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

Example

Triangle begins:
1,
3,1,
9,4,1,
29,13,5,1,
99,42,18,6,1,
351,141,60,24,7,1,
1275,492,201,84,31,8,1,

Mathematica

Select[Flatten[Table[Sum[Binomial[n-i, k]Binomial[2i, i], {i, 0, n}], {n, 0, 10}, {k, 0, 10}]], #!=0&] (* Harvey P. Dale, Jul 05 2012 *)

Prog

(Maxima) create_list(sum(binomial(n-i, k)*binomial(2*i, i), i, 0, n), n, 0, 8, k, 0, n);

Crossrefs

Sequence in context: A285280 A285266 A067417 * A016577 A308704 A270702

Adjacent sequences: A187884 A187885 A187886 * A187888 A187889 A187890

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, Mar 15 2011

Extensions

Mathematica program corrected by Harvey P. Dale, Jul 05 2012

Comment added and comment corrected by Michel Marcus, Jun 23 2013

Status

approved