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A111126 Triangle read by rows: T(k,s) = binomial(k+s,2s+1)*(2k-1)*(2k+1)/(2s+3), k >= 1, 0 <= s <= k-1. 1
1, 10, 3, 35, 28, 5, 84, 126, 54, 7, 165, 396, 297, 88, 9, 286, 1001, 1144, 572, 130, 11, 455, 2184, 3510, 2600, 975, 180, 13, 680, 4284, 9180, 9350, 5100, 1530, 238, 15, 969, 7752, 21318, 28424, 20995, 9044, 2261, 304, 17, 1330, 13167, 45144, 76076, 72618 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

K. Dilcher and K. B. Stolarsky, A Pascal-type triangle characterizing twin primes, Amer. Math. Monthly, 112 (2005), 673-681.

EXAMPLE

Triangle starts:

1;

10,3;

35,28,5;

84,126,54,7;

165,396,297,88,9;

MAPLE

T:=(k, s)->binomial(k+s, 2*s+1)*(2*k-1)*(2*k+1)/(2*s+3): for k from 1 to 10 do seq(T(k, s), s=0..k-1) od; # yields sequence in triangular form; Emeric Deutsch, Feb 01 2006

CROSSREFS

Mirror image of A111127. Cf. A111125, A082985, A100218, A098599.

Sequence in context: A050100 A103219 A260680 * A165790 A077194 A038305

Adjacent sequences:  A111123 A111124 A111125 * A111127 A111128 A111129

KEYWORD

nonn,easy,tabl

AUTHOR

N. J. A. Sloane, Oct 16 2005

EXTENSIONS

More terms from Emeric Deutsch, Feb 01 2006

STATUS

approved

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Last modified February 18 12:10 EST 2020. Contains 332018 sequences. (Running on oeis4.)