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A053525 E.g.f.: (1-x)/(2-exp(x)). 4
1, 0, 1, 4, 23, 166, 1437, 14512, 167491, 2174746, 31374953, 497909380, 8619976719, 161667969646, 3265326093109, 70663046421208, 1631123626335707, 40004637435452866, 1038860856732399105, 28476428717448349996, 821656049857815980455 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.4(a).

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

Jean-Christophe Aval, Adrien Boussicault, Philippe Nadeau, Tree-like Tableaux, Electronic Journal of Combinatorics, 20(4), 2013, #P34.

Venkatesan Guruswami, Enumerative aspects of certain subclasses of perfect graphs, Discrete Math. 205 (1999), 97-117. See Th. 6.3.

FORMULA

a(n) ~ n!/2 * (1-log(2))/(log(2))^(n+1). - Vaclav Kotesovec, Dec 08 2012

BINOMIAL transform is A005840. - Michael Somos, Aug 01 2016

a(n) = Sum_{k=0..n-1} binomial(n, k) * a(k), n>1. - Michael Somos, Aug 01 2016

a(n) = A005840(n) / 2, n>1. - Michael Somos, Aug 01 2016

E.g.f. A(x) satisfies (1 - x) * A'(x) = A(x) * (x - 2 + 2*A(x)). - Michael Somos, Aug 01 2016

EXAMPLE

G.f. = 1 + x^2 + 4*x^3 + 23*x^4 + 166*x^5 + 1437*x^6 + 14512*x^7 + ...

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(1-x)/(2-Exp[x]), {x, 0, nn}], x] Range[0, nn]!] Harvey P. Dale, May 17 2012

PROG

(PARI) {a(n) = if( n<0, 0, n! * polcoeff( (1 - x) / (2 - exp(x + x*O(x^n))), n))}; /* Michael Somos, Aug 01 2016 */

CROSSREFS

a(n)=c(n)-n*c(n-1) where c() = A000670.

Cf. A005840, A052882.

Sequence in context: A171992 A158884 A317057 * A277382 A208676 A317276

Adjacent sequences:  A053522 A053523 A053524 * A053526 A053527 A053528

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified November 20 08:16 EST 2018. Contains 317385 sequences. (Running on oeis4.)