login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A338435 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = n!*LaguerreL(n, -k*n). 1
1, 1, 1, 1, 2, 2, 1, 3, 14, 6, 1, 4, 34, 168, 24, 1, 5, 62, 654, 2840, 120, 1, 6, 98, 1626, 17688, 61870, 720, 1, 7, 142, 3246, 59928, 616120, 1649232, 5040, 1, 8, 194, 5676, 151064, 2844120, 26252496, 51988748, 40320, 1, 9, 254, 9078, 318744, 9052120, 165100752, 1322624016, 1891712384, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

FORMULA

T(n,k) = Sum_{j=0..n} (k*n)^j * (n-j)! * binomial(n,j)^2.

T(n,k) = n! * [x^n] exp(k*n*x/(1-x))/(1-x).

T(n,k) = A289192(n,k*n).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, ...

1, 2, 3, 4, 5, ...

2, 14, 34, 62, 98, ...

6, 168, 654, 1626, 3246, ...

24, 2840, 17688, 59928, 151064, ...

MATHEMATICA

T[n_, k_] := n! * LaguerreL[n, -k*n]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 05 2021 *)

PROG

(PARI) T(n, k) = sum(j=0, n, (k*n)^j*(n-j)!*binomial(n, j)^2);

(PARI) T(n, k) = n!*pollaguerre(n, 0, -k*n); \\ Michel Marcus, Feb 05 2021

CROSSREFS

Columns k=0..8 gives A000142, A277373, A277391, A277392, A277418, A277419, A277420, A277421, A277422.

Main diagonal gives A340863.

Cf. A021009, A289192 (n!*LaguerreL(n, -k)), A341014.

Sequence in context: A258222 A112324 A061531 * A214722 A071430 A092514

Adjacent sequences: A338432 A338433 A338434 * A338436 A338437 A338438

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Feb 05 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 10:23 EST 2022. Contains 358630 sequences. (Running on oeis4.)