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A354309 Expansion of e.g.f. 1/(1 - 2*x)^(x/2). 4
1, 0, 2, 6, 44, 360, 3744, 46200, 662864, 10838016, 198943200, 4050937440, 90613710912, 2208677328000, 58265734055424, 1653914478303360, 50263564166365440, 1628300694034022400, 56012708047907510784, 2039053421375533094400, 78314004507947110456320 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=2..n} k * 2^(k-2)/(k-1) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-2*k) * |Stirling1(n-k,k)|/(n-k)!.
a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 1/4) / (Gamma(1/4) * exp(n)). - Vaclav Kotesovec, Mar 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x)^(x/2)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*2^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*abs(stirling(n-k, k, 1))/(n-k)!);
CROSSREFS
Sequence in context: A342986 A136589 A077048 * A277479 A120594 A038180
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 23 2022
STATUS
approved

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Last modified April 23 16:40 EDT 2024. Contains 371916 sequences. (Running on oeis4.)