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!)
A335111 a(n) = n! * Sum_{k=0..n-1} (-2)^k / k!. 0
0, 1, -2, 6, -8, 40, 48, 784, 5248, 49536, 490240, 5403904, 64822272, 842742784, 11798284288, 176974510080, 2831591636992, 48137058942976, 866467058614272, 16462874118651904, 329257482362552320, 6914407129635618816, 152116956851937476608, 3498690007594658430976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inverse binomial transform of A000240.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f.: Sum_{k>=1} k! * x^k / (1 + 2*x)^(k + 1).

E.g.f.: x*exp(-2*x) / (1 - x).

a(n) = A000023(n) - A122803(n).

MATHEMATICA

Table[n! Sum[(-2)^k/k!, {k, 0, n - 1}], {n, 0, 23}]

nmax = 23; CoefficientList[Series[Sum[k! x^k/(1 + 2 x)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 23; CoefficientList[Series[x Exp[-2 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

PROG

(PARI) a(n) = n! * sum(k=0, n-1, (-2)^k / k!); \\ Michel Marcus, May 23 2020

CROSSREFS

Cf. A000023, A000240, A066534, A087981, A122803.

Sequence in context: A152158 A291782 A327271 * A095239 A192009 A065953

Adjacent sequences:  A335108 A335109 A335110 * A335112 A335113 A335115

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 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 August 12 07:38 EDT 2020. Contains 336438 sequences. (Running on oeis4.)