A219532 O.g.f. satisfies: A(x) = Sum_{n>=0} n^n*(n+1)^(n-1) * exp(-n*(n+1)*x/A(x)) * (x/A(x))^n / n!.

1, 1, 3, 28, 427, 9096, 248298, 8258552, 323891811, 14636853712, 749171687006, 42853503567480, 2710099789775566, 187811949192251632, 14156747168376595956, 1153316446792123524144, 100995199848878125787555, 9461277820648354922926368, 944228520086488255850280918

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Example

O.g.f.: A(x) = 1 + x + 3*x^2 + 28*x^3 + 427*x^4 + 9096*x^5 + 248298*x^6 +...
where
A(x) = 1 + 1^1*2^0*exp(-1*2*x/A(x))*x/A(x) + 2^2*3^1*exp(-2*3*x/A(x))*x^2/A(x)^2/2! + 3^3*4^2*exp(-3*4*x/A(x))*x^3/A(x)^3/3! + 4^4*5^3*exp(-4*5*x/A(x))*x^4/A(x)^4/4! + 5^5*6^4*exp(-5*6*x)*x^5/A(x)/5! +...

Prog

(PARI) {a(n)=local(A=1); for(i=1, n, A=sum(m=0, n, m^m*(m+1)^(m-1)*(x/A)^m*exp(-m*(m+1)*x/A+x*O(x^n))/m!)); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A217900.

Sequence in context: A298696 A359917 A143636 * A376034 A319369 A340789

Adjacent sequences: A219529 A219530 A219531 * A219533 A219534 A219535

Keyword

nonn

Author

Paul D. Hanna, Nov 21 2012

Status

approved