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!)
A127548 O.g.f.: Sum_{n>=0} n!*(x/(1+x)^2)^n. 2
1, 1, 0, 1, 4, 19, 112, 771, 6088, 54213, 537392, 5867925, 69975308, 904788263, 12607819040, 188341689287, 3002539594128, 50878366664393, 913161208490016, 17304836525709097, 345279674107957524, 7235298537356113339 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n+1) = inverse binomial transform of A013999 = Sum_{k=0..n)}binomial(n,k)*(-1)^(n-k)*A013999(k). - Emanuele Munarini, Jul 01 2013

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..450

FORMULA

a(n) = Sum_{s=1..n} (-1)^(n-s)*s!*C(s+n-1,2s-1) if n>=1, where C(a,b)=binomial(a,b). - R. J. Mathar, Jul 13 2007

G.f.: Q(0) where Q(k) = 1 + (2*k + 1)*x/( (1+x)^2- 2*x*(1+x)^2*(k+1)/(2*x*(k+1) + (1+x)^2/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Mar 08 2013

a(n) = A000271(n) + A000271(n-1). - Peter Bala, Sep 02 2016

a(n) ~ exp(-2) * n!. - Vaclav Kotesovec, Oct 31 2017

MAPLE

A127548 := proc(n) if n = 0 then 1 ; else add(factorial(s)*(-1)^(n-s)*binomial(s+n-1, 2*s-1), s=1..n) ; fi ; end: for n from 0 to 20 do printf("%d, ", A127548(n)) ; od ; # R. J. Mathar, Jul 13 2007

MATHEMATICA

nn = 21; CoefficientList[Series[Sum[n!*(x/(1 + x)^2)^n, {n, 0, nn}], {x, 0, nn}], x] (* Michael De Vlieger, Sep 04 2016 *)

PROG

(Python)

import math

def binomial(n, m):

...a=1

...for k in range(n-m+1, n+1):

......a *= k

...return a//math.factorial(m)

def A127548(n):

...if n == 0:

......return 1

...a=0

...for s in range(1, n+1):

......a += (-1)**(n-s)*binomial(s+n-1, 2*s-1)*math.factorial(s)

...return a

for n in range(0, 30):

...print(A127548(n))

# R. J. Mathar, Oct 20 2009

CROSSREFS

Cf. A000179, A078480, A013999, A000271, A000904, A078509.

Sequence in context: A060905 A304473 A174123 * A331326 A122835 A013185

Adjacent sequences:  A127545 A127546 A127547 * A127549 A127550 A127551

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jun 27 2007

EXTENSIONS

More terms from R. J. Mathar, Jul 13 2007

More terms from R. J. Mathar, Oct 20 2009

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 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)