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A119400 a(n) = Sum_{k=0..n} (n!/k!)^2*binomial(n,k). 4
1, 2, 13, 172, 3809, 126526, 5874517, 362848088, 28744087297, 2839192902874, 341922922464701, 49297062811573732, 8380916229314577313, 1658770724530766046422, 378056469777362366873989, 98286603829297813268996176, 28907477297195536067142301697 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1-x)))/(1-x).

Recurrence: a(n)=(3*n^2-3*n+2)*a(n-1)-3*(n-1)^4*a(n-2)+(n-2)^3*(n-1)^3*a(n-3). - Vaclav Kotesovec, Sep 30 2012

a(n) ~ 1/sqrt(3)*n^(2*n+2/3)/exp(2*n-3*n^(1/3)). - Vaclav Kotesovec, Sep 30 2012

E.g.f.: exp(x) * Sum_{n>=0} x^n/n!^3  =  Sum_{n>=0} a(n)*x^n/n!^3. - Paul D. Hanna, Nov 27 2012

MATHEMATICA

Table[Sum[(n!/k!)^2*Binomial[n, k], {k, 0, n}], {n, 0, 16}] (* Stefan Steinerberger, Jun 17 2007 *)

PROG

(PARI) a(n)=n!^3*polcoeff(exp(x+x*O(x^n))*sum(m=0, n, x^m/m!^3), n)

for(n=0, 25, print1(a(n), ", ")) \\ Paul D. Hanna, Nov 27 2012

CROSSREFS

Cf. A000522, A002720, A216831.

Sequence in context: A143851 A088316 A006905 * A182314 A268988 A183606

Adjacent sequences:  A119397 A119398 A119399 * A119401 A119402 A119403

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jul 25 2006

EXTENSIONS

More terms from Stefan Steinerberger, Jun 17 2007

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)