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A307996 Expansion of e.g.f. exp(1 - exp(x)*(1 - 2*x)). 0
1, 1, 4, 15, 73, 410, 2591, 18165, 139266, 1155509, 10293729, 97815520, 986113613, 10499247005, 117603042220, 1381191356979, 16958788930317, 217132031279842, 2892337840164051, 40002168264724193, 573363461815952802, 8502905138072937073, 130268705062115090965, 2058969680487762098496 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} (2*k - 1)*binomial(n-1,k-1)*a(n-k).

MATHEMATICA

nmax = 23; CoefficientList[Series[Exp[1 - Exp[x] (1 - 2 x)], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = Sum[(2 k - 1) Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

CROSSREFS

Cf. A000248, A000354, A003727, A005408, A275707.

Sequence in context: A303229 A340355 A356009 * A230741 A020082 A020037

Adjacent sequences: A307993 A307994 A307995 * A307997 A307998 A307999

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 09 2019

STATUS

approved

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Last modified December 3 20:26 EST 2022. Contains 358543 sequences. (Running on oeis4.)