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A073178 a(n) = n!^2 times coefficient of x^n in e^(x*(3-x)/2/(1-x))/(1-x)^(1/2). 2
1, 2, 13, 180, 4266, 153180, 7725510, 519629040, 44880355800, 4835536256880, 635221698211800, 99872627051181600, 18507444606249152400, 3990439472567239692000, 990119486841576670378800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.65(b).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

e^(x*(3-x)/2/(1-x))/(1-x)^(1/2) = Sum_{n>=0} a(n)*x^n/n!^2. - Vladeta Jovovic, Aug 01 2006

a(n) ~ sqrt(Pi)*n^(2*n+1/2)*exp(2*sqrt(n)-2*n). - Vaclav Kotesovec, Apr 21 2014

MATHEMATICA

CoefficientList[Series[E^(x*(3-x)/2/(1-x))/(1-x)^(1/2), {x, 0, 20}], x] * Range[0, 20]!^2 (* Vaclav Kotesovec, Apr 21 2014 *)

PROG

(PARI) a(n)=if(n<0, 0, n!^2*polcoeff(exp(x*(3-x)/2/(1-x)+x*O(x^n))/sqrt(1-x+x*O(x^n)), n))

CROSSREFS

Cf. A049088.

Sequence in context: A183606 A307655 A137610 * A193192 A226865 A062156

Adjacent sequences:  A073175 A073176 A073177 * A073179 A073180 A073181

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 19 2002

STATUS

approved

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Last modified October 16 03:15 EDT 2019. Contains 328038 sequences. (Running on oeis4.)