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A086614 Triangle read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x)^2 + xy*f(x,y)^2. 2
1, 2, 1, 3, 4, 2, 4, 10, 12, 5, 5, 20, 42, 40, 14, 6, 35, 112, 180, 140, 42, 7, 56, 252, 600, 770, 504, 132, 8, 84, 504, 1650, 3080, 3276, 1848, 429, 9, 120, 924, 3960, 10010, 15288, 13860, 6864, 1430, 10, 165, 1584, 8580, 28028, 57330, 73920, 58344, 25740 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..53.

FORMULA

T(n,k) = binomial(2*k, k-1)*binomial(n+k+1, n-k) / k for k > 0. # Peter Luschny, Jan 26 2018

EXAMPLE

Rows:

{1},

{2, 1},

{3, 4,    2},

{4, 10,  12,    5},

{5, 20,  42,   40,   14},

{6, 35, 112,  180,  140,   42},

{7, 56, 252,  600,  770,  504,  132},

{8, 84, 504, 1650, 3080, 3276, 1848, 429}, ...

MAPLE

T := (n, k) -> `if`(k=0, n+1, binomial(2*k, k-1)*binomial(n+k+1, n-k)/k):

for n from 0 to 8 do seq(T(n, k), k=0..n) od; # Peter Luschny, Jan 26 2018

CROSSREFS

T(n,n) = A000108(n).

Cf. A086615 (antidiagonal sums), A086616 (row sums), A086617.

Sequence in context: A208532 A245334 A102756 * A108959 A208750 A107893

Adjacent sequences:  A086611 A086612 A086613 * A086615 A086616 A086617

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 24 2003

STATUS

approved

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Last modified November 30 18:40 EST 2020. Contains 338807 sequences. (Running on oeis4.)