VOOZH about

URL: https://oeis.org/A119304

⇱ A119304 - OEIS

login
A119304
Triangle read by rows: T(n,k) = binomial(4n-k,n-k), 0 <= k <= n.
3
1, 4, 1, 28, 7, 1, 220, 55, 10, 1, 1820, 455, 91, 13, 1, 15504, 3876, 816, 136, 16, 1, 134596, 33649, 7315, 1330, 190, 19, 1, 1184040, 296010, 65780, 12650, 2024, 253, 22, 1, 10518300, 2629575, 593775, 118755, 20475, 2925, 325, 25, 1, 94143280, 23535820
OFFSET
0,2
LINKS
Indranil Ghosh, Rows 0..125, flattened
FORMULA
Riordan array (1/(1-4f(x)),f(x)) where f(x)(1-f(x))^3 = x.
From Peter Bala, Jun 04 2024: (Start)
'Horizontal' recurrence equation: T(n, 0) = binomial(4*n,n) and for k >= 1, T(n, k) = Sum_{i = 1..n+1-k} i*(i+1)/2 * T(n-1, k-2+i).
T(n, k) = Sum_{j = 0..n} binomial(n+j-1, j)*binomial(3*n-k-j, 2*n). (End)
EXAMPLE
Triangle begins
1;
4, 1;
28, 7, 1;
220, 55, 10, 1;
1820, 455, 91, 13, 1;
15504, 3876, 816, 136, 16, 1;
134596, 33649, 7315, 1330, 190, 19, 1;
MATHEMATICA
Flatten[Table[Binomial[4n-k, n-k], {n, 0, 9}, {k, 0, n}]] (* Indranil Ghosh, Feb 26 2017 *)
PROG
(PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1(binomial(4*n-k, n-k), ", "); ); print(); ); } \\ Indranil Ghosh, Feb 26 2017
(Python)
from sympy import binomial
i=0
for n in range(12):
for k in range(n+1):
print(str(i)+" "+str(binomial(4*n-k, n-k)))
i+=1 # Indranil Ghosh, Feb 26 2017
CROSSREFS
Rows sums are A052203. First column is A005810. Inverse of A119305.
Sequence in context: A134150 A134151 A264773 * A114150 A392228 A134149
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, May 13 2006
STATUS
approved