|
| |
|
|
A025262
|
|
a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4.
|
|
6
| |
|
|
1, 1, 1, 3, 8, 23, 68, 207, 644, 2040, 6558, 21343, 70186, 232864, 778550, 2620459, 8872074, 30195288, 103246502, 354508628, 1221846856, 4225644866, 14659644348, 51002664023, 177909901566, 622093882290, 2180123564130, 7656055966092
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
LINKS
| M. Somos, Number Walls in Combinatorics.
|
|
|
FORMULA
| G.f.: (1 - sqrt(1 - 4*x + 4*x^3)) / 2. Satisfies A(x) - A(x)^2 = x - x^3 - Michael Somos, Aug 04, 2000.
Comment from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 27 2008: Given an integer t >= 1 and initial values u = [a_0, a_1, ..., a_{t-1}], we may define an infinite sequence Phi(u) by setting a_n = a_{n-1} + a_0*a_{n-1} + a_1*a_{n-2} + ... + a_{n-2}*a_1 for n >= t. For example Phi([1]) is the Catalan numbers A000108. The present sequence is Phi([1,1,1]).
Row sums of A176703 if offset 0. - Michael Somos, Jan 09 2012
a(n+2) = A056010(n) if n >= 0.
|
|
|
EXAMPLE
| x + x^2 + x^3 + 3*x^4 + 8*x^5 + 23*x^6 + 68*x^7 + 207*x^8 + 644*x^9 +
...
|
|
|
PROG
| (PARI) {a(n) = polcoeff( (1 - sqrt(1 - 4*x + 4*x^3 + x * O(x^n))) / 2, n)} /* Michael Somos, Aug 04 2000 */
|
|
|
CROSSREFS
| Cf. A176703, A056010.
Sequence in context: A199103 A057198 * A056010 A002712 A192679 A193418
Adjacent sequences: A025259 A025260 A025261 * A025263 A025264 A025265
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
| |
|
|
