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A258993 Triangle read by rows: T(n,k) = binomial(n+k,n-k), k = 0..n-1. 10
1, 1, 3, 1, 6, 5, 1, 10, 15, 7, 1, 15, 35, 28, 9, 1, 21, 70, 84, 45, 11, 1, 28, 126, 210, 165, 66, 13, 1, 36, 210, 462, 495, 286, 91, 15, 1, 45, 330, 924, 1287, 1001, 455, 120, 17, 1, 55, 495, 1716, 3003, 3003, 1820, 680, 153, 19, 1, 66, 715, 3003, 6435, 8008, 6188, 3060, 969, 190, 21 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(n,k) = A085478(n,k) = A007318(A094727(n),A004736(k)), k = 0..n-1;

rounded(T(n,k)/(2*k+1)) = A258708(n,k);

rounded(sum(T(n,k)/(2*k+1)): k = 0..n-1) = A000967(n).

LINKS

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

EXAMPLE

.  n\k |  0  1    2    3     4     5     6     7    8    9  10 11

. -----+-----------------------------------------------------------

.   1  |  1

.   2  |  1  3

.   3  |  1  6    5

.   4  |  1 10   15    7

.   5  |  1 15   35   28     9

.   6  |  1 21   70   84    45    11

.   7  |  1 28  126  210   165    66    13

.   8  |  1 36  210  462   495   286    91    15

.   9  |  1 45  330  924  1287  1001   455   120   17

.  10  |  1 55  495 1716  3003  3003  1820   680  153   19

.  11  |  1 66  715 3003  6435  8008  6188  3060  969  190  21

.  12  |  1 78 1001 5005 12870 19448 18564 11628 4845 1330 231 23  .

PROG

(Haskell)

a258993 n k = a258993_tabl !! (n-1) !! k

a258993_row n = a258993_tabl !! (n-1)

a258993_tabl = zipWith (zipWith a007318) a094727_tabl a004736_tabl

CROSSREFS

If a diagonal of 1's is added on the right, this becomes A085478.

Cf. A007318, A004736, A094727.

Cf. A027941 (row sums), A117671 (central terms), A143858, A000967, A258708.

T(n,k): A000217 (k=1), A000332 (k=2), A000579 (k=3), A000581 (k=4), A001287 (k=5), A010965 (k=6), A010967 (k=7), A010969 (k=8), A010971 (k=9), A010973 (k=10), A010975 (k=11), A010977 (k=12), A010979 (k=13), A010981 (k=14), A010983 (k=15), A010985 (k=16), A010987 (k=17), A010989 (k=18), A010991 (k=19), A010993 (k=20), A010995 (k=21), A010997 (k=22), A010999 (k=23), A011001 (k=24), A017714 (k=25), A017716 (k=26), A017718 (k=27), A017720 (k=28), A017722 (k=29), A017724 (k=30), A017726 (k=31), A017728 (k=32), A017730 (k=33), A017732 (k=34), A017734 (k=35), A017736 (k=36), A017738 (k=37), A017740 (k=38), A017742 (k=39), A017744 (k=40), A017746 (k=41), A017748 (k=42), A017750 (k=43), A017752 (k=44), A017754 (k=45), A017756 (k=46), A017758 (k=47), A017760 (k=48), A017762 (k=49), A017764 (k=50).

T(n+k,n): A005408 (k=1), A000384 (k=2), A000447 (k=3), A053134 (k=4), A002299 (k=5), A053135 (k=6), A053136 (k=7), A053137 (k=8), A053138 (k=9), A196789 (k=10).

Cf. A165253.

Sequence in context: A061702 A112351 A143858 * A109954 A153641 A133545

Adjacent sequences:  A258990 A258991 A258992 * A258994 A258995 A258996

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Jun 22 2015

STATUS

approved

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Last modified February 19 08:51 EST 2018. Contains 299330 sequences. (Running on oeis4.)