A118794 E.g.f.: 1 - exp((-1 + sqrt(5 - 4*exp(x)) )/2).

0, 1, 2, 11, 121, 1902, 38381, 945989, 27552260, 925920081, 35265751869, 1501219998148, 70632987480771, 3639861179067661, 203881981765871618, 12333901891547136559, 801418950244634922973, 55665376886060309513990

Offset

0,3

Comments

Also equals the row sums of triangle A118793 (offset without leading zero).

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (n-1)!*Sum_{k=0..n-1} [x^k] (x/log(1-x-x^2))^n/(n-1-k)! for n>0.

a(n) = sum(m=1..n, ((-1)^(m+1)*sum(k=0..n-m, ((k+m-1)!*binomial(2*k+m-1,k+m-1)*stirling2(n,k+m))))/(m-1)!). - Vladimir Kruchinin, Jul 02 2011

a(n) ~ sqrt(5/2) * n^(n-1) / (2 * exp(n+1/2) * (log(5/4))^(n-1/2)). - Vaclav Kotesovec, Jul 31 2014

Example

E.g.f.: A(x) = x + 2/2*x^2 + 11/6*x^3 + 121/24*x^4 + 1902/120*x^5 + ...

Mathematica

With[{nn=20}, CoefficientList[Series[1-Exp[(Sqrt[5-4Exp[x]]-1)/2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 07 2014 *)

Prog

(PARI) {a(n)=local(x=X+X^2*O(X^n)); n!*polcoeff(1-exp((-1+sqrt(5-4*exp(x)))/2), n, X)}
for(n=0, 30, print1(a(n), ", "))
(PARI) /* As the row sums of A118793: */
{a(n)=local(x=X+X^2*O(X^n)); if(n<1, 0, -(n-1)!*sum(k=0, n-1, polcoeff(((x/log(1-x-x^2)))^n/(n-1-k)!, k, X)))}
for(n=0, 30, print1(a(n), ", "))
(Maxima)
a(n):=sum(((-1)^(m+1)*sum(((k+m-1)!*binomial(2*k+m-1, k+m-1)*stirling2(n, k+m)), k, 0, n-m))/(m-1)!, m, 1, n); /* Vladimir Kruchinin, Jul 02 2011 */

Crossrefs

Cf. A118793, A118795.

Sequence in context: A057076 A346650 A251663 * A222879 A354978 A247736

Adjacent sequences: A118791 A118792 A118793 * A118795 A118796 A118797

Keyword

nonn

Author

Paul D. Hanna, Apr 30 2006

Status

approved