The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360481

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A360481

E.g.f. satisfies A(x) = x * exp(x + 2 * A(x)).
(history; published version)

#14 by Vaclav Kotesovec at Fri Feb 17 15:02:45 EST 2023

STATUS

editing

approved

#13 by Vaclav Kotesovec at Fri Feb 17 15:02:40 EST 2023

FORMULA

a(n) ~ sqrt(1 + LambertW(exp(-1)/2)) * n^(n-1) / (2 * LambertW(exp(-1)/2)^n * exp(n)). - Vaclav Kotesovec, Feb 17 2023

STATUS

approved

editing

#12 by Michael De Vlieger at Thu Feb 09 09:38:41 EST 2023

STATUS

proposed

approved

#11 by Seiichi Manyama at Thu Feb 09 09:34:20 EST 2023

STATUS

editing

proposed

#10 by Seiichi Manyama at Thu Feb 09 09:34:07 EST 2023

CROSSREFS

Cf. A360471A360473.

STATUS

proposed

editing

#9 by Seiichi Manyama at Thu Feb 09 08:01:54 EST 2023

STATUS

editing

proposed

#8 by Seiichi Manyama at Thu Feb 09 07:09:59 EST 2023

FORMULA

E.g.f.: A(x) = -LambertW(-2*x * exp(x))/2.

a(n) = Sum_{k=1..n} 2^(k-1) * k^(n-1) * binomial(n,k).

#7 by Seiichi Manyama at Thu Feb 09 07:07:46 EST 2023

DATA

0, 1, 6, 63, 1044, 23805, 692118, 24482115, 1020584232, 49000005945, 2662853279850, 161586078510879, 10830019921469532, 794577001293803637, 63339899145968483262, 5451312770064188283195, 503784284643602483767632, 49757423537114340032969073

#6 by Seiichi Manyama at Thu Feb 09 06:52:44 EST 2023

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

#5 by Seiichi Manyama at Thu Feb 09 06:47:30 EST 2023

CROSSREFS

Cf. A216857, A360482, A360483, A360484.

Cf. A360471.