A141617 Triangle T(n,m) = prime(m)*prime(n-m)*binomial(n,m) read by rows, 0<=m<=n.

1, 2, 2, 3, 8, 3, 5, 18, 18, 5, 7, 40, 54, 40, 7, 11, 70, 150, 150, 70, 11, 13, 132, 315, 500, 315, 132, 13, 17, 182, 693, 1225, 1225, 693, 182, 17, 19, 272, 1092, 3080, 3430, 3080, 1092, 272, 19, 23, 342, 1836, 5460, 9702, 9702, 5460, 1836, 342, 23

Offset

0,2

Comments

For the purpose of this sequence define prime(0)=1.

Row sums are 1, 4, 14, 46, 148, 462, 1420, 4234, 12356, 34726, 95220,...

Links

Table of n, a(n) for n=0..54.

Formula

Symmetry: T(n,m) = T(n,n-m).

Example

   1;
   2,   2;
   3,   8,    3;
   5,  18,   18,     5;
   7,  40,   54,    40,     7;
  11,  70,  150,   150,    70,    11;
  13, 132,  315,   500,   315,   132,    13;
  17, 182,  693,  1225,  1225,   693,   182,    17;
  19, 272, 1092,  3080,  3430,  3080,  1092,   272,   19;
  23, 342, 1836,  5460,  9702,  9702,  5460,  1836,  342,  23;
  29, 460, 2565, 10200, 19110, 30492, 19110, 10200, 2565, 460, 29;
  ...

Maple

p:= n-> `if`(n=0, 1, ithprime(n)):
T:= (n, k)-> binomial(n, k)*p(k)*p(n-k):
seq(seq(T(n, k), k=0..n), n=0..10);  # Alois P. Heinz, Apr 26 2023

Mathematica

Table[Table[If[n == m ==0, 1, If[m == 0 || m == n, Prime[n], (Prime[n - m]*Prime[m])*Binomial[n, m]]], {m, 0, n}], {n, 0, 10}] Flatten[%]

Crossrefs

Cf. A008578, A098350.

Sequence in context: A135835 A177696 A134574 * A267644 A204197 A238654

Adjacent sequences: A141614 A141615 A141616 * A141618 A141619 A141620

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 23 2008

Status

approved