A344049 a(n) = KummerU(-2*n, 1, -n).

1, 7, 648, 173007, 91356544, 80031878175, 104921038236672, 192311632290456007, 469591293625846038528, 1473442955416649975287959, 5776758846811567983984640000, 27673221072138317786331655146207, 159045755874087839794327707061321728, 1080096259061106512089015938295879551727

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = (2*n)! * LaguerreL(2*n, -n).

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

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

a(n) ~ 2^(4*n + 1) * n^(2*n) / (sqrt(3) * exp(n)). - Vaclav Kotesovec, May 09 2021

Maple

egf := n -> exp(n*x/(1-x))/(1-x): ser := n -> series(egf(n), x, 32):
a := n -> (2*n)!*coeff(ser(n), x, 2*n): seq(a(n), n = 0..13);

Mathematica

a[n_] := HypergeometricU[-2 n, 1, -n];
Table[a[n], {n, 0, 13}]

Prog

(SageMath)
@cached_function
def L(n, x):
    if n == 0: return 1
    if n == 1: return 1 - x
    return (L(n-1, x) * (2*n-1-x) - L(n-2, x)*(n-1))/n
A344049 = lambda n: factorial(2*n)*L(2*n, -n)
print([A344049(n) for n in (0..13)])
(PARI)
a(n) = (2*n)! * sum(j=0, 2*n, binomial(2*n, j) * n^j / j!)
for(n=0, 13, print(a(n)))

Crossrefs

a(n) = A344048(2*n, n).

Sequence in context: A052134 A101811 A092326 * A347507 A074282 A171737

Adjacent sequences: A344046 A344047 A344048 * A344050 A344051 A344052

Keyword

nonn

Author

Peter Luschny, May 08 2021

Status

approved