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A094715 a(n) = sum(2i+3j=n, 0<=i<=n, 0<=j<=n, n!/((2i)!(3j)!)). 2
1, 0, 1, 1, 1, 10, 2, 35, 29, 85, 211, 220, 926, 1001, 3095, 5461, 9829, 25126, 37130, 97223, 164921, 349525, 728575, 1309528, 2973350, 5326685, 11450531, 22369621, 43942081, 91869970, 174174002, 365088395, 708653429, 1431655765, 2884834891 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Average of binomial and inverse binomial transform of 1,0,0,1,0,0,1,... - Paul Barry, Jan 04 2005

LINKS

Table of n, a(n) for n=0..34.

FORMULA

limit n --> infty a(n)/2^n=1/6

G.f.: (x^5+2*x^2+x^3-x^4-1)/(2*x-1)/(3*x^2+3*x+1)/(x^2-x+1). - Vladeta Jovovic, May 23 2004

a(n)=sum{k=0..floor(n/2), C(n, 2k)(2cos(2*Pi*(n-2k)/3+1)/3} - Paul Barry, Jan 04 2005

E.g.f.: (exp(z)+2*exp(-z/2)*cos(z*sqrt(3/4)))*cosh(z)/3. - Peter Luschny, Jul 10 2012

MAPLE

A094715_list := proc(n) local i; (exp(z)+2*exp(-z/2)*cos(z*sqrt(3/4)))*cosh(z)/3;  series(%, z, n+2): seq(i!*coeff(%, z, i), i=0..n) end: A094715_list(34); # Peter Luschny, Jul 10 2012

PROG

(PARI) a(n)=sum(i=0, n, sum(j=0, n, if(n-2*i-3*j, 0, n!/(2*i)!/(3*j)!)))

CROSSREFS

Cf. A024493, A094717.

Sequence in context: A262557 A030595 A232590 * A213555 A305995 A096043

Adjacent sequences:  A094712 A094713 A094714 * A094716 A094717 A094718

KEYWORD

nonn

AUTHOR

Benoit Cloitre, May 23 2004

STATUS

approved

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Last modified June 21 16:32 EDT 2021. Contains 345365 sequences. (Running on oeis4.)