A252501 Triangle T read by rows: T(n,k) = binomial(2*n+1,k)*binomial(n,k), n>=0, 0<=k<=n.

1, 1, 3, 1, 10, 10, 1, 21, 63, 35, 1, 36, 216, 336, 126, 1, 55, 550, 1650, 1650, 462, 1, 78, 1170, 5720, 10725, 7722, 1716, 1, 105, 2205, 15925, 47775, 63063, 35035, 6435, 1, 136, 3808, 38080, 166600, 346528, 346528, 155584, 24310

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Marc Chamberland and Karl Dilcher, A Binomial Sum Related to Wolstenholme's Theorem, J. Number Theory, Vol. 171, Issue 11 (Nov. 2009), pp. 2659-2672 (see Thm. 2.3).

Example

Triangle T begins:
.1
.1.....3
.1....10.....10
.1....21.....63......35
.1....36....216.....336......126
.1....55....550....1650.....1650......462
.1....78...1170....5720....10725.....7722.....1716
.1...105...2205...15925....47775....63063....35035.....6435
.1...136...3808...38080...166600...346528...346528...155584...24310

Mathematica

Flatten[Table[Binomial[2*n + 1, k]*Binomial[n, k], {n, 0, 8}, {k, 0, n}]] (* Replace Flatten[] with Grid[] to get the triangle. *)

Crossrefs

Cf. A000012 (col. 1), A014105 (col. 2), A001700 (diag), A045721 (row sums).

Cf. A234839, A252355.

Sequence in context: A264491 A144697 A185419 * A281000 A146154 A068438

Adjacent sequences: A252498 A252499 A252500 * A252502 A252503 A252504

Keyword

nonn,tabl

Author

L. Edson Jeffery, Dec 17 2014

Status

approved