A144297 BINOMIAL transform of A001515.

1, 3, 12, 65, 465, 4212, 46441, 604389, 9071250, 154267865, 2931801639, 61578273462, 1416474723373, 35415138314415, 956276678789100, 27733572777976973, 859779201497486829, 28373745267763162716, 993110842735800666085, 36746019445535955976665

Offset

0,2

Links

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

N. J. A. Sloane, Transforms

Formula

From Vaclav Kotesovec, Oct 20 2012: (Start)

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

Recurrence: a(n) = (2*n+1)*a(n-1) - (4*n-5)*a(n-2) + 2*(n-2)*a(n-3).

a(n) ~ 2^(n+1/2)*n^n/exp(n-3/2). (End)

a(n) = Sum_{j=0..n} binomial(n,j)*A001515(j). - G. C. Greubel, Sep 28 2023

Mathematica

CoefficientList[Series[E^(1+x-Sqrt[1-2*x])/Sqrt[1-2*x], {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Oct 20 2012 *)

Prog

(Magma) I:=[1, 3, 12]; [n le 3 select I[n] else (2*n-1)*Self(n-1) -(4*n-9)*Self(n-2) +2*(n-3)*Self(n-3): n in [1..30]]; // G. C. Greubel, Sep 28 2023
(SageMath)
def A144297_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( exp(1+x-sqrt(1-2*x))/sqrt(1-2*x) ).egf_to_ogf().list()
A144297_list(40) # G. C. Greubel, Sep 28 2023

Crossrefs

Cf. A001515.

Sequence in context: A109577 A368265 A242575 * A007017 A183273 A082987

Adjacent sequences: A144294 A144295 A144296 * A144298 A144299 A144300

Keyword

nonn

Author

N. J. A. Sloane, Dec 04 2008

Status

approved