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A238761 Subtriangle of the generalized ballot numbers, T(n,k) = A238762(2*k-1,2*n-1), 1<=k<=n, read by rows. 2
1, 2, 3, 3, 8, 10, 4, 15, 30, 35, 5, 24, 63, 112, 126, 6, 35, 112, 252, 420, 462, 7, 48, 180, 480, 990, 1584, 1716, 8, 63, 270, 825, 1980, 3861, 6006, 6435, 9, 80, 385, 1320, 3575, 8008, 15015, 22880, 24310, 10, 99, 528, 2002, 6006, 15015, 32032, 58344, 87516, 92378 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n,n) = A001700(n-1).

T(n,n-1) = A162551(n-1).

EXAMPLE

[n\k 1   2    3    4    5    6     7 ]

[1]  1,

[2]  2,  3,

[3]  3,  8,  10,

[4]  4, 15,  30,  35,

[5]  5, 24,  63, 112, 126,

[6]  6, 35, 112, 252, 420,  462,

[7]  7, 48, 180, 480, 990, 1584, 1716.

MAPLE

binom2 := proc(n, k) local h;

   h := n -> (n-((1-(-1)^n)/2))/2;

   n!/(h(n-k)!*h(n+k)!) end:

A238761 := (n, k) -> binom2(n+k, n-k+1)*(n-k+1)/(n+k):

seq(print(seq(A238761(n, k), k=1..n)), n=1..7);

PROG

(Sage)

@CachedFunction

def ballot(p, q):

    if p == 0 and q == 0: return 1

    if p < 0 or p > q: return 0

    S = ballot(p-2, q) + ballot(p, q-2)

    if q % 2 == 1: S += ballot(p-1, q-1)

    return S

A238761 = lambda n, k: ballot(2*k-1, 2*n-1)

for n in (1..7): [A238761(n, k) for k in (1..n)]

CROSSREFS

Row sums are A002054.

Cf. A001700, A009766.

Sequence in context: A161136 A258163 A108381 * A261469 A292498 A108692

Adjacent sequences:  A238758 A238759 A238760 * A238762 A238763 A238764

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Mar 05 2014

STATUS

approved

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Last modified October 18 04:09 EDT 2018. Contains 316304 sequences. (Running on oeis4.)