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A032109 "BIJ" (reversible, indistinct, labeled) transform of 1,1,1,1... 3
1, 1, 2, 7, 38, 271, 2342, 23647, 272918, 3543631, 51123782, 811316287, 14045783798, 263429174191, 5320671485222, 115141595488927, 2657827340990678, 65185383514567951, 1692767331628422662 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Starting (1, 2, 7, 38, 271,...) = A008292 * [1, 1, 2, 4, 8,...] [From Gary W. Adamson, Dec 25 2008]

The inverse binomial transform is 1, 0, 1, 3, 19, 135, 1171, 11823, 136459,.. , see A091346. - R. J. Mathar, Oct 17 2012

LINKS

R. J. Mathar, Table of n, a(n) for n = 0..100

C. G. Bower, Transforms (2)

FORMULA

E.g.f.: (e^(2*x)-2*e^x-1)/(2*e^x-4).

a(n) = (A000670(n)+1)/2. - Vladeta Jovovic, Apr 13 2003

MAPLE

A032109 := proc(n)

    (A000670(n)+1)/2 ;

end proc: # R. J. Mathar, Oct 17 2012

PROG

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

(PARI) list(n)=my(v=Vec(subst((1-y^2/2)/(1-y), y, exp(x+x*O(x^n))-1))); vector(n+1, i, v[i]*(i-1)!) \\ Charles R Greathouse IV, Oct 17 2012

CROSSREFS

A000629, A000670, A002050, A032109, A052856, A076726 are all more-or-less the same sequence. - N. J. A. Sloane, Jul 04 2012

A052856(n)=2*a(n), if n>0.

Cf. A008292.

Sequence in context: A094431 A209006 A168492 * A088792 A114160 A145159

Adjacent sequences:  A032106 A032107 A032108 * A032110 A032111 A032112

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified December 19 12:22 EST 2014. Contains 252224 sequences.