A257501 Triangle, read by rows, T(n,k) = 2*k*C(2*(n+k),n-k)/(n+k).

1, 4, 1, 14, 8, 1, 48, 44, 12, 1, 165, 208, 90, 16, 1, 572, 910, 544, 152, 20, 1, 2002, 3808, 2907, 1120, 230, 24, 1, 7072, 15504, 14364, 7084, 2000, 324, 28, 1, 25194, 62016, 67298, 40480, 14625, 3248, 434, 32, 1, 90440, 245157, 303600

Offset

1,2

Links

Indranil Ghosh, Rows 1..125, flattened

Formula

G.f.: 1/(1-(C(x)-1)^2*y/x)-1, where C(x) is g.f. of Catalan numbers (A000108).

Example

1;
4, 1;
14, 8, 1;
48, 44, 12, 1;
165, 208, 90, 16, 1;

Mathematica

Flatten@ Table[2 k Binomial[2 (n + k), n - k]/(n + k), {n, 10}, {k, n}] (* Michael De Vlieger, Apr 27 2015 *)

Prog

(Maxima)
T(n, k):=(2*k*binomial(2*(n+k), n-k))/(n+k);
(Magma) /* Us triangle */ [[(2*k*Binomial(2*(n+k), n-k))/(n+k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Apr 27 2015
(PARI)
tabl(nn) = {for (n=1, nn, for(k=1, n, print1(2*k*binomial(2*(n+k), n-k)/(n+k), ", "); ); print(); ); };
tabl(10); \\ Indranil Ghosh, Mar 04 2017
(Python)
import math
f=math.factorial
def C(n, r): return f(n)/f(r)/f(n-r)
i=1
for n in range(1, 126):
....for k in range(1, n+1):
........print str(i)+" "+str(2*k*C(2*(n+k), n-k)/(n+k))
........i+=1 # Indranil Ghosh, Mar 04 2017

Crossrefs

Cf. A000108.

Sequence in context: A191584 A231185 A187055 * A096644 A145829 A016115

Adjacent sequences: A257498 A257499 A257500 * A257502 A257503 A257504

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 27 2015

Status

approved