OFFSET
0,5
COMMENTS
Row sums are: {1, 2, 8, 32, 467, 1553, 19778, 84254, 1457381, 87864065, 354929117, ...}.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, Use of combinatorial algebra for diffusion on fractals, Physical Review A, volume 34, Number 3 (1986) p. 2503 (7b).
FORMULA
T(n,k) = binomial(prime(n+1) - 1, prime(k+1) - 1) with T(n,0) = 1.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 6, 1;
1, 15, 15, 1;
1, 45, 210, 210, 1;
1, 66, 495, 924, 66, 1;
1, 120, 1820, 8008, 8008, 1820, 1;
1, 153, 3060, 18564, 43758, 18564, 153, 1;
1, 231, 7315, 74613, 646646, 646646, 74613, 7315, 1;
MAPLE
seq(seq( `if`(k=0, 1, binomial(ithprime(n+1)-1, ithprime(k+1)-1) ), k=0..n), n=0..10); # G. C. Greubel, Dec 02 2019
MATHEMATICA
T[n_, k_]:= If[k==0, 1, Binomial[Prime[n+1] -1, Prime[k+1] -1]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(PARI) T(n, k) = if(k==0, 1, binomial(prime(n+1)-1, prime(k+1)-1) ); \\ G. C. Greubel, Dec 02 2019
(Magma) [k eq 0 select 1 else Binomial(NthPrime(n+1)-1, NthPrime(k+1)-1): k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 02 2019
(Sage)
def T(n, k):
if (k==0): return 1
else: return binomial(nth_prime(n+1)-1, nth_prime(k+1)-1)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 02 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jan 13 2009
EXTENSIONS
Edited by G. C. Greubel, Dec 02 2019
STATUS
approved