|
| |
|
|
A172389
|
|
a(n) = Sum_{k=0..n} C(n,k)*3^(k*(n-k))/2^n.
|
|
1
|
|
|
|
1, 1, 2, 7, 44, 481, 9272, 310087, 18164624, 1843946881, 326808099872, 100310221406407, 53656068398769344, 49686835289802328801, 80090696216400251499392, 223445962168511596412895367
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
Table of n, a(n) for n=0..15.
|
|
|
FORMULA
|
O.g.f.: A(x) = Sum_{n>=0} 2*x^n/(2 - 3^n*x)^(n+1).
E.g.f.: E(x) = Sum_{n>=0} exp(3^n*x/2)*(x/2)^n/n!.
a(n) = A135079(n)/2^n.
|
|
|
EXAMPLE
|
O.g.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 481*x^5 + 9272*x^6 +...
A(x) = 2/(2-x) + 2*x/(2-3*x)^2 + 2*x^2/(2-3^2*x)^3 + 2*x^3/(2-3^3*x)^4 +...+ 2*x^n/(2-3^n*x)^(n+1) +...
E.g.f.: E(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 44*x^4/4! + 481*x^5/5! +...
E(x) = exp(x/2) + exp(3*x/2)*x/2 + exp(3^2*x/2)*(x/2)^2/2! + exp(3^3*x/2)*(x/2)^3/3! +...+ exp(3^n*x/2)*(x/2)^n/n! +...
|
|
|
PROG
|
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*3^(k*(n-k)))/2^n}
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(3^k*x/2 +x*O(x^n))*(x/2)^k/k!), n)}
(PARI) {a(n)=polcoeff(sum(k=0, n, (x/2)^k/(1-3^k*x/2 +x*O(x^n))^(k+1)), n)}
|
|
|
CROSSREFS
|
Cf. variants: A135079, A047863.
Sequence in context: A194453 A001046 A158257 * A153522 A107354 A006118
Adjacent sequences: A172386 A172387 A172388 * A172390 A172391 A172392
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Paul D. Hanna, Feb 03 2010
|
|
|
STATUS
|
approved
|
| |
|
|
