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!)
A343832 a(n) = Sum_{k=0..n} k! * binomial(n,k) * binomial(2*n+1,k). 7
1, 4, 31, 358, 5509, 106096, 2456299, 66471826, 2059640713, 71920704124, 2794938616471, 119653108240414, 5595650767265101, 283841520215780008, 15523069639558351459, 910529206043204428426, 57023540590242398853649, 3797750659849704886903156, 268025698704886063968108943 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..365

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

FORMULA

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

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

a(n) = n! * LaguerreL(n, n+1, -1).

a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n+2).

a(n) == 1 (mod 3).

a(n) ~ 2^(2*n + 3/2) * n^n / exp(n-1). - Vaclav Kotesovec, May 02 2021

MAPLE

a := n -> add(k!*binomial(n, k)*binomial(2*n+1, k), k=0..n):

a := n -> n!*add(binomial(2*n+1, k)/(n-k)!, k=0..n):

a := n -> (-1)^n*KummerU(-n, n+2, -1):

a := n -> n!*LaguerreL(n, n+1, -1): # Peter Luschny, May 02 2021

MATHEMATICA

a[n_] := Sum[k! * Binomial[n, k] * Binomial[2*n+1, k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, May 01 2021 *)

Table[(-1)^n * HypergeometricU[-n, 2 + n, -1], {n, 0, 20}] (* Vaclav Kotesovec, May 02 2021 *)

PROG

(PARI) a(n) = sum(k=0, n, k!*binomial(n, k)*binomial(2*n+1, k));

(PARI) a(n) = (2*n+1)!*sum(k=0, n, binomial(n, k)/(k+n+1)!);

(PARI) a(n) = n!*sum(k=0, n, binomial(2*n+1, k)/(n-k)!);

(PARI) a(n) = n!*pollaguerre(n, n+1, -1);

CROSSREFS

Cf. A000522, A045721, A082545, A152059, A248668, A343830, A343831.

Sequence in context: A321031 A102757 A295254 * A145561 A201628 A086677

Adjacent sequences:  A343829 A343830 A343831 * A343833 A343834 A343835

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 01 2021

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 November 28 16:42 EST 2021. Contains 349413 sequences. (Running on oeis4.)