|
| |
|
|
A181136
|
|
G.f.: A(x) = Sum_{n>=0} x^n/[Sum_{k=0..n} C(n,k)^3*(-x)^k].
|
|
1
|
|
|
|
1, 1, 2, 10, 92, 1264, 26138, 753322, 28451978, 1385043022, 84971475986, 6393154081582, 580295829204452, 62818032904371952, 8005929383232314294, 1187186361565313907994, 203034917331580351972520
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Compare the g.f. of this sequence to the identity:
(1-x)/(1-2*x) = Sum_{n>=0} x^n/[Sum_{k=0..n} C(n,k)*(-x)^k].
|
|
|
LINKS
|
Robert Israel, Table of n, a(n) for n = 0..248
|
|
|
FORMULA
|
G.f.: Sum_{n>=0} x^n/hypergeom([-n,-n,-n],[1,1],x). - Robert Israel, Dec 24 2017
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 92*x^4 + 1264*x^5 +...
which equals the series:
A(x) = 1 + x/(1-x) + x^2/(1-2^3*x+x^2) + x^3/(1-3^3*x+3^3*x^2-x^3) + x^4/(1-4^3*x+6^3*x^2-4^3*x^3+x^4) + x^5/(1-5^3*x+10^3*x^2-10^3*x^3+5^3*x^4-x^5) +...
|
|
|
MAPLE
|
G:= add(x^n/hypergeom([-n, -n, -n], [1, 1], x), n=0..50):
S:= series(G501, x, 51):
seq(coeff(S, x, n), n=0..50); # Robert Israel, Dec 24 2017
|
|
|
PROG
|
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/sum(k=0, m, binomial(m, k)^3*(-x)^k+x*O(x^n))), n)}
|
|
|
CROSSREFS
|
Cf. A178324.
Sequence in context: A095937 A277380 A108528 * A182952 A108209 A111773
Adjacent sequences: A181133 A181134 A181135 * A181137 A181138 A181139
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Paul D. Hanna, Jan 25 2011
|
|
|
STATUS
|
approved
|
| |
|
|
