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A108704 Number of partitions of 112233...nn into n pairs. 1
1, 1, 4, 18, 126, 1110, 12120, 156660, 2341500, 39701340, 752839920, 15785181720, 362606123880, 9055825538760, 244296192460320, 7079382509799600, 219321853964413200, 7233629128601475600, 253054306933115688000, 9358989706213886138400, 364860828050107348159200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Laszlo Lovasz, Combinatorial Problems and Solutions, AMS Chelsea Publishing, American Mathematical Society.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..400

FORMULA

E.g.f.: exp(x*x/2)/sqrt(1-2*x).

a(n) ~ 2^(n+1/2)*n^n/exp(n-1/8). - Vaclav Kotesovec, Sep 26 2013

a(n) = 2^n*(n-1/2)!*2F2((1-n)/2,-n/2;1/4 -n/2,3/4 - n/2; 1/8)/sqrt(Pi). - Benedict W. J. Irwin, May 25 2016

Conjecture: a(n) +(-2*n+1)*a(n-1) +(-n+1)*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Jun 08 2016

EXAMPLE

Partitions of 1122 into 2 pairs: 11 22, 12 12, 12 21, 21 21 = 4 partitions so a(2)=4.

MAPLE

a:= n-> n! *coeff(series(exp(x*x/2)/sqrt(1-2*x), x, n+1), x, n):

seq (a(n), n=0..20);

MATHEMATICA

CoefficientList[Series[E^(x*x/2)/Sqrt[1-2*x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 26 2013 *)

PROG

(PARI) x='x+O('x^50); Vec(serlaplace(exp(x*x/2)/sqrt(1-2*x))) \\ G. C. Greubel, May 24 2017

CROSSREFS

Cf. A002135.

Sequence in context: A317377 A215691 A073511 * A001423 A308351 A291335

Adjacent sequences:  A108701 A108702 A108703 * A108705 A108706 A108707

KEYWORD

nonn

AUTHOR

Miklos Kristof, Jun 20 2005

STATUS

approved

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Last modified February 20 19:57 EST 2020. Contains 332084 sequences. (Running on oeis4.)