A266487 E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N - n)^(2*n) * (x/N)^n/n! ]^(1/N).

1, 1, -3, 31, -559, 14541, -496811, 21081859, -1070585055, 63366015673, -4285932328819, 326248732427751, -27610580638457807, 2572239828612623365, -261621661000490429211, 28849626308051995285771, -3428690784657696770593471, 436924188109882619766249201, -59432725217403244945921112675, 8595527924368773785463788378287, -1317123285394547040368548520041839, 213171869078193696050387803319525821, -36338236299957647745418230431675850763, 6507698606647750492700809995200106342675, -1221579456277487714539848255959245396739999

Offset

0,3

Comments

Compare to: Limit_{N->oo} [ Sum_{n>=0} (N + n)^n * x^n/n! ]^(1/N) = Sum_{n>=0} (n+1)^(n-1) * x^n/n!.

Links

Table of n, a(n) for n=0..24.

Example

 E.g.f.: A(x) = 1 + x - 3*x^2/2! + 31*x^3/3! - 559*x^4/4! + 14541*x^5/5! - 496811*x^6/6! + 21081859*x^7/7! - 1070585055*x^8/8! + 63366015673*x^9/9! - 4285932328819*x^10/10! +...
where A(x) equals the limit, as N -> oo, of the series
[1 + (N-1)^2*(x/N) + (N-2)^4*(x/N)^2/2! + (N-3)^6*(x/N)^3/3! + (N-4)^8*(x/N)^4/4! + (N-5)^10*(x/N)^5/5! + (N-6)^12*(x/N)^6/6! +...]^(1/N).

Prog

 (PARI) /* Informal listing of terms 0..30 */
\p300
H(n) = sum(k=0, 32, (n - k)^(2*k) * x^k/k! +O(x^32))
Vec( round( serlaplace( subst(H(10^100)^(1/10^100), x, x/10^100) )*1.) )

Crossrefs

Cf. A266481, A266482, A266483, A266484, A266485, A266486.

Sequence in context: A360343 A261471 A273378 * A229258 A319896 A370260

Adjacent sequences: A266484 A266485 A266486 * A266488 A266489 A266490

Keyword

sign

Author

Paul D. Hanna, Dec 30 2015

Status

approved