A338995 Triangle T(n,m):=binomial(n+3*m+2,n-m).

1, 3, 1, 6, 7, 1, 10, 28, 11, 1, 15, 84, 66, 15, 1, 21, 210, 286, 120, 19, 1, 28, 462, 1001, 680, 190, 23, 1, 36, 924, 3003, 3060, 1330, 276, 27, 1, 45, 1716, 8008, 11628, 7315, 2300, 378, 31, 1, 55, 3003, 19448, 38760, 33649, 14950, 3654, 496, 35, 1, 66, 5005, 43758, 116280, 134596, 80730, 27405, 5456, 630, 39, 1

Offset: 0

Author

Vladimir Kruchinin, Nov 17 2020

Keywords

• nonn
• tabl

Comments

Riordan Array (1/(1-x)^3,x/(1-x)).

Sum_{m=0..n} T(n,m) = A055990(n-1).

Examples

			1,
3, 1,
6, 7, 1,
10, 28, 11, 1,
15, 84, 66, 15, 1,
21, 210, 286, 120, 19, 1,
28, 462, 1001, 680, 190, 23, 1
		

Crossrefs

Cf. A000217 (1st column), A007318, A055990 (row sums).

Formula

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