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A338037 Triangle T(n,m) = C(2*m-1,m)*C(n+2*m-1,n-m). 1
1, 0, 1, 0, 3, 3, 0, 6, 18, 10, 0, 10, 63, 90, 35, 0, 15, 168, 450, 420, 126, 0, 21, 378, 1650, 2730, 1890, 462, 0, 28, 756, 4950, 12740, 15120, 8316, 1716, 0, 36, 1386, 12870, 47775, 85680, 79002, 36036, 6435, 0, 45, 2376, 30030, 152880, 385560, 526680, 396396, 154440, 24310 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

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

EXAMPLE

1,

0, 1,

0, 3, 3,

0, 6, 18, 10,

0, 10, 63, 90, 35,

0, 15, 168, 450, 420, 126,

0, 21, 378, 1650, 2730, 1890, 462

MATHEMATICA

T[n_, m_] := Binomial[2*m - 1, m] * Binomial[n + 2*m - 1, n - m]; Table[T[n, m], {n, 0, 9}, {m, 0, n}] // Flatten (* Amiram Eldar, Oct 08 2020 *)

PROG

(Maxima)

T(n, m):=binomial(2*m-1, m)*binomial(n+2*m-1, n-m);

CROSSREFS

Cf. A000217, A001700, A253942.

Sequence in context: A122831 A019701 A134813 * A164107 A093755 A176276

Adjacent sequences:  A338034 A338035 A338036 * A338038 A338039 A338040

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Oct 08 2020

STATUS

approved

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Last modified August 1 07:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)