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A200965 Triangle T(n,k) = coefficient of x^n in expansion of ((1-sqrt(1-4*x))/((1-x)*2))^k = sum(n>=k, T(n,k) * x^n). 1
1, 2, 1, 4, 4, 1, 9, 12, 6, 1, 23, 34, 24, 8, 1, 65, 98, 83, 40, 10, 1, 197, 294, 273, 164, 60, 12, 1, 626, 919, 891, 612, 285, 84, 14, 1, 2056, 2974, 2938, 2188, 1195, 454, 112, 16, 1, 6918, 9891, 9846, 7698, 4677, 2118, 679, 144, 18, 1, 23714, 33604, 33549 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Triangle T(n,k)=

1. Riordan Array (1,(1-sqrt(1-4*x))/((1-x)*2)) without first column.

2. Riordan Array ((1-sqrt(1-4*x))/((1-x)*2*x),(1-sqrt(1-4*x))/((1-x)*2)) numbering triangle (0,0).

Convolution triangle of A014137(n). - Philippe Deléham, Jan 23 2014

LINKS

Table of n, a(n) for n=1..58.

FORMULA

T(n,k):=k*sum(i=0..n-k, (binomial(i+k-1,k-1)*binomial(2*(n-i)-k-1,n-i-1))/(n-i)).

EXAMPLE

Triangle:

1,

2, 1,

4, 4, 1,

9, 12, 6, 1,

23, 34, 24, 8, 1,

65, 98, 83, 40, 10, 1,

197, 294, 273, 164, 60, 12, 1

PROG

(Maxima)

T(n, k):=k*sum((binomial(i+k-1, k-1)*binomial(2*(n-i)-k-1, n-i-1))/(n-i), i, 0, n-k);

CROSSREFS

Cf. Columns: A014137, A014143

Sequence in context: A209240 A263989 A202710 * A117427 A097761 A200756

Adjacent sequences:  A200962 A200963 A200964 * A200966 A200967 A200968

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Nov 25 2011

STATUS

approved

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)