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A187887 Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)). 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums are A082590.
First column is A006134.
LINKS
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
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)