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A339028 Triangle T(n,m) = 3*(m+1)*C(n+m+3,m)*C(2*n+2,n-m)/((n+m+3)*(C(n+1,m)). 0
1, 3, 3, 9, 12, 9, 28, 42, 42, 28, 90, 144, 162, 144, 90, 297, 495, 594, 594, 495, 297, 1001, 1716, 2145, 2288, 2145, 1716, 1001, 3432, 6006, 7722, 8580, 8580, 7722, 6006, 3432, 11934, 21216, 27846, 31824, 33150, 31824, 27846, 21216, 11934, 41990, 75582, 100776, 117572, 125970, 125970, 117572, 100776, 75582, 41990 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..54.

FORMULA

G.f. ((sqrt(1-4*x*y)-sqrt(1-4*x))/(2*(x-x*y)))^3.

EXAMPLE

1,

3,3,

9,12,9,

28,42,42,28,

90,144,162,144,

90,297,495,594,594,495,297

PROG

(Maxima)

T(n, m):=if n<m then 0 else (3*(m+1)*(binomial(n+m+3, m))*(binomial(2*n+2, n-m)))/((n+m+3)*(binomial(n+1, m)));

CROSSREFS

Cf. A000108, A000245, A002057 (row sums), A168256, A120406,

Sequence in context: A124281 A320293 A146153 * A173048 A165992 A117153

Adjacent sequences:  A339025 A339026 A339027 * A339029 A339030 A339031

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Nov 20 2020

STATUS

approved

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Last modified April 20 05:46 EDT 2021. Contains 343121 sequences. (Running on oeis4.)