OFFSET
1,2
COMMENTS
The n-triangular honeycomb rook graph is the disjoint union of the complete graphs K_k for k in {1..n}. In terms of a triangular chessboard it is the graph for a chesspiece that is constrained to move on a single axis. - Andrew Howroyd, Jul 17 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
FORMULA
a(n) = Product_{k=1..n} A000085(k). - Andrew Howroyd, Jul 17 2017
log(a(n)) ~ n^2*log(n)/4 - 3*n^2/8 + 2*n^(3/2)/3. - Vaclav Kotesovec, Aug 29 2023
MATHEMATICA
FoldList[Times, Table[HypergeometricPFQ[{-k/2, (1 - k)/2}, {}, 2], {k, 20}]] (* Eric W. Weisstein, Jul 19 2017 *)
Table[(-1/2)^(Binomial[n + 1, 2]/2) Product[HermiteH[k, -I/Sqrt[2]], {k, n}], {n, 20}] (* Eric W. Weisstein, Jul 19 2017 *)
Table[Product[HypergeometricPFQ[{-k/2, (1 - k)/2}, {}, 2], {k, n}], {n, 20}] (* Eric W. Weisstein, Jul 19 2017 *)
PROG
(PARI)
a(n) = prod(k=1, n, k! * polcoeff( exp( x + x^2 / 2 + x * O(x^k)), k)); \\ Andrew Howroyd, Jul 17 2017
(Python)
from math import prod, factorial
def A289897(n): return prod(sum(factorial(k)//(factorial(k-(m<<1))*factorial(m)*(1<<m)) for m in range((k>>1)+1)) for k in range(1, n+1)) # Chai Wah Wu, Aug 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 14 2017
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jul 17 2017
STATUS
approved