login
A294349
Product of first n terms of the binomial transform of the Lucas numbers (A000032).
0
2, 6, 42, 756, 35532, 4370436, 1407280392, 1186337370456, 2618246576596392, 15128228719573952976, 228844715840995186667952, 9062937281450932377610903056, 939663463215395570775453650652192, 255065069445576619918001465293982953056
OFFSET
0,1
FORMULA
a(n) ~ c * phi^(n*(n+1)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio and c = 2.349094356918735309421297337651771419003525539652230102934874983942...
MATHEMATICA
Table[Product[Sum[Binomial[m, k]*LucasL[k], {k, 0, m}], {m, 0, n}], {n, 0, 15}]
Table[Product[LucasL[2*k], {k, 0, n}], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 29 2017
STATUS
approved