login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A331660 E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 - x)) * A(x/(1 - x)). 1
1, 1, 5, 32, 280, 3280, 49480, 927560, 21037640, 566134160, 17803754560, 646052181520, 26757321804880, 1252934215973600, 65791336312915520, 3846554938702140320, 248841434876849499040, 17713758333248102781760, 1380631354206969100115200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..19.

FORMULA

a(1) = 1; a(n+1) = Sum_{k=0..n-1} binomial(n,k)^2 * k! * a(n-k).

MATHEMATICA

terms = 20; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + 1/(1 - x) A[x/(1 - x) + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x] Range[0, terms]! // Rest

a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k]^2 k! a[n - k - 1], {k, 0, n - 2}]; Table[a[n], {n, 1, 20}]

CROSSREFS

Cf. A001063, A110083, A132228, A331661.

Sequence in context: A265130 A305407 A320349 * A001923 A257710 A305305

Adjacent sequences:  A331657 A331658 A331659 * A331661 A331662 A331663

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 23 2020

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 February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)