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A344049 a(n) = KummerU(-2*n, 1, -n). 2
1, 7, 648, 173007, 91356544, 80031878175, 104921038236672, 192311632290456007, 469591293625846038528, 1473442955416649975287959, 5776758846811567983984640000, 27673221072138317786331655146207, 159045755874087839794327707061321728, 1080096259061106512089015938295879551727 (list; graph; refs; listen; history; text; internal format)
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 * A074282 A171737 A013568

Adjacent sequences:  A344046 A344047 A344048 * A344050 A344051 A344052

KEYWORD

nonn

AUTHOR

Peter Luschny, May 08 2021

STATUS

approved

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Last modified August 4 12:33 EDT 2021. Contains 346447 sequences. (Running on oeis4.)