A277413 E.g.f.: Series_Reversion( x + Sum_{n>=2} (-1)^(n-1) * x^(2*n-1)/(n*(n-1)) ) = Sum_{n>=1} a(n)*x^(2*n-1)/(2*n-1)!.

1, 3, 70, 4620, 599256, 128648520, 41281606080, 18507916627200, 11049593741746560, 8474451191616009600, 8119493428719228192000, 9504049395027168805824000, 13345312208487981260926464000, 22140681034117932250214874624000, 42846437958647788197412779939840000, 95657301566159892238019686222356480000, 244038306493164073323605513327887380480000

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

E.g.f.: A(x) = x + 3*x^3/3! + 70*x^5/5! + 4620*x^7/7! + 599256*x^9/9! + 128648520*x^11/11! + 41281606080*x^13/13! + 18507916627200*x^15/15! +...
such that
Series_Reversion(A(x)) = x - x^3/(1*2) + x^5/(2*3) - x^7/(3*4) + x^9/(4*5) - x^11/(5*6) + x^13/(6*7) +...+ (-1)^(n-1)*x^(2*n-1)/(n*(n-1)) +...

Prog

(PARI) {a(n) = (2*n-1)! * polcoeff( serreverse(x - sum(m=2, n, (-1)^m * x^(2*m-1) / (m*(m-1)) ) +O(x^(2*n+2))), 2*n-1)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Sequence in context: A000282 A322775 A338408 * A210920 A140048 A135951

Adjacent sequences: A277410 A277411 A277412 * A277414 A277415 A277416

Keyword

nonn

Author

Paul D. Hanna, Nov 17 2016

Status

approved