login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A206397 E.g.f. A(x) = series reversion of log(1+x)-x^3/3. 0
1, 1, 3, 21, 171, 1821, 24123, 373941, 6693291, 135897741, 3081969243, 77250233061, 2120715880011, 63277499072061, 2039050439495163, 70571948084252181, 2610905715855178731, 102824333281385113581 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n)=(sum(k=0..n-1, (n+k-1)!*sum(j=0..k, (-1)^j/(k-j)!*sum(i=0..min(j,(n+j-1)/3),(1/i!)*(-1)^i* stirling1(n-3*i+j-1,j-i)/(3^i*(n-3*i+j-1)!))))), n>0.

a(n) ~ n^(n-1) / (sqrt(s*(2+s^3)) * exp(n) * r^(n-1/2)), where s = 1/3*(-1 + (25/2 - (3*sqrt(69))/2)^(1/3) + (1/2*(25 + 3*sqrt(69)))^(1/3)) = 0.75487766624669276... is the root of the equation s^2*(1+s) = 1 and r = log(1+s) - s^3/3 = 0.4190125789786... - Vaclav Kotesovec, Jan 22 2014

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[Log[1+x]-x^3/3, {x, 0, 20}], x], x]*Range[0, 20]!] (* Vaclav Kotesovec, Jan 22 2014 *)

PROG

(Maxima) a(n):=(sum((n+k-1)!*sum((-1)^j/(k-j)!*sum((1/i!)*(-1)^i*stirling1(n-3*i+j-1, j-i)/(3^i*(n-3*i+j-1)!), i, 0, min(j, (n+j-1)/3)), j, 0, k), k, 0, n-1));

CROSSREFS

Sequence in context: A189475 A206178 A233861 * A247480 A228923 A287995

Adjacent sequences:  A206394 A206395 A206396 * A206398 A206399 A206400

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Feb 07 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)