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!)
A062147 Row sums of unsigned triangle A062137 (generalized a=3 Laguerre). 6
1, 5, 31, 229, 1961, 19081, 207775, 2501801, 32989969, 472630861, 7307593151, 121247816845, 2148321709561, 40476722545169, 807927483311551, 17028146983530961, 377844723929464865, 8803698102396787861, 214877019857456672479, 5482159931449737760181 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for sequences related to Laguerre polynomials

FORMULA

E.g.f.: exp(x/(1-x))/(1-x)^4.

a(n) = Sum_{m=0..n} n!*binomial(n+3, n-m)/m!.

a(n) = (2*n+3)*a(n-1) - (n-1)*(n+2)*a(n-2). - Vaclav Kotesovec, Oct 11 2012

a(n) ~ exp(2*sqrt(n)-n-1/2)*n^(n+7/4)/sqrt(2). - Vaclav Kotesovec, Oct 11 2012

MATHEMATICA

Table[Sum[n!*Binomial[n+3, n-k]/k!, {k, 0, n}], {n, 0, 20}]

(* or *)

Table[n!*SeriesCoefficient[E^(x/(1-x))/(1-x)^4, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 11 2012 *)

PROG

(PARI) x='x+O('x^66); Vec(serlaplace(exp(x/(1-x))/(1-x)^4)) \\ Joerg Arndt, May 06 2013

(MAGMA) [Factorial(n)*(&+[Binomial(n+3, n-m)/Factorial(m): m in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018

CROSSREFS

Sequence in context: A192950 A001910 A052773 * A213048 A069321 A211179

Adjacent sequences:  A062144 A062145 A062146 * A062148 A062149 A062150

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

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 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)