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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 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.)