|
| |
|
|
A001756
|
|
a(n) = A059366(n,n-3) = A059366(n,3) for n >= 3, where the triangle A059366 arises from the expansion of a trigonometric integral.
(Formerly M4967 N2131)
|
|
2
|
|
|
|
15, 60, 450, 4500, 55125, 793800, 13097700, 243243000, 5016886875, 113716102500, 2808787731750, 75071235739500, 2158298027510625, 66409170077250000, 2177272076104125000, 75769068248423550000, 2789248824895091934375, 108288483790044745687500
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
3,1
|
|
|
COMMENTS
|
Previous name was: Expansion of an integral.
|
|
|
REFERENCES
|
L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 166-167.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = n! * Sum_{k=0..n-3} (-1)^k * 2^(2*k-n) * binomial(n-3, k) * binomial(2*n-2*k, n-3) * binomial(n-2*k+3, n-k) for n >= 3. [Special case of a formula by Comtet, but corrected]
a(n) = 20 * binomial(2*n-6, n-3) * n!/2^n for n >= 3. [Special case of a formula due to Reinhard Zumkeller]
a(n) = binomial(-1/2, 3) * binomial(-1/2, n-3) * (-1)^n * n! * 2^n for n >= 3. (End)
|
|
|
MATHEMATICA
|
RecurrenceTable[{a[3]==15, a[n]==a[n-1]n (2n-7)/(n-3)}, a, {n, 20}] (* Harvey P. Dale, Nov 08 2011 *)
Join[{c = 15}, Table[c = c*n*(2*n - 7)/(n - 3), {n, 4, 20}]] (* T. D. Noe, Aug 10 2012 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
