A187888 Riordan matrix (1/sqrt(1-4*x),x/(1-x)).

1, 2, 1, 6, 3, 1, 20, 9, 4, 1, 70, 29, 13, 5, 1, 252, 99, 42, 18, 6, 1, 924, 351, 141, 60, 24, 7, 1, 3432, 1275, 492, 201, 84, 31, 8, 1, 12870, 4707, 1767, 693, 285, 115, 39, 9, 1, 48620, 17577, 6474, 2460, 978, 400, 154, 48, 10, 1, 184756, 66197, 24051, 8934, 3438, 1378, 554, 202, 58, 11, 1

Offset

0,2

Links

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

Formula

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

a(n,k) = sum(M(k,n-k-i)*binomial(2*i,i),i=0..n-k) where M(n,k) = n*(n+1)*(n+2)...(n+k-1)/k!.

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

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

Example

Triangle begins:
1
2,1
6,3,1
20,9,4,1
70,29,13,5,1
252,99,42,18,6,1
924,351,141,60,24,7,1
3432,1275,492,201,84,31,8,1

Prog

(Maxima) M(n, k):=pochhammer(n, k)/k!;
create_list(sum(M(k, n-k-i)*binomial(2*i, i), i, 0, n-k), n, 0, 8, k, 0, n);

Crossrefs

A187887

Sequence in context: A168151 A213221 A180281 * A239102 A239103 A246971

Adjacent sequences: A187885 A187886 A187887 * A187889 A187890 A187891

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, Mar 15 2011

Status

approved