A338435 - OEIS

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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, 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).