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A107105 Triangle, read by rows, where T(n,k) = C(n,k)*(C(n,k) + 1)/2, n>=k>=0. 1
1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 21, 10, 1, 1, 15, 55, 55, 15, 1, 1, 21, 120, 210, 120, 21, 1, 1, 28, 231, 630, 630, 231, 28, 1, 1, 36, 406, 1596, 2485, 1596, 406, 36, 1, 1, 45, 666, 3570, 8001, 8001, 3570, 666, 45, 1, 1, 55, 1035, 7260, 22155, 31878, 22155, 7260 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Replace each number x in Pascal's triangle by x(x+1)/2. - Charlie Marion, May 31 2013

LINKS

Table of n, a(n) for n=0..62.

FORMULA

n-th row sum equals A005317(n) = (C(2n, n) + 2^n)/2.

EXAMPLE

Triangle begins:

1;

1,1;

1,3,1;

1,6,6,1;

1,10,21,10,1;

1,15,55,55,15,1;

1,21,120,210,120,21,1;

1,28,231,630,630,231,28,1; ...

PROG

(PARI) T(n, k)=binomial(n, k)*(binomial(n, k)+1)/2

CROSSREFS

Cf. A005317 (row sums), A107597 (antidiagonal sums).

Sequence in context: A162745 A001263 A162747 * A088925 A100862 A098568

Adjacent sequences:  A107102 A107103 A107104 * A107106 A107107 A107108

KEYWORD

nonn,tabl,easy

AUTHOR

Paul D. Hanna, May 21 2005

STATUS

approved

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Last modified October 23 22:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)