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 A081673 Expansion of exp(3*x) - exp(x)*(1-BesselI_0(2*x)). 4
 1, 3, 11, 33, 99, 293, 869, 2579, 7667, 22821, 68001, 202799, 605229, 1807263, 5399195, 16136513, 48243347, 144275093, 431573297, 1291258319, 3864163769, 11565703931, 34622195135, 103656406949, 310377872861, 929465445743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A081672. LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 FORMULA E.g.f. exp(3*x) - exp(x)*(1-BesselI_0(2*x)). Conjecture: n*(2*n - 7)*a(n) +(-12*n^2 + 50*n - 33)*a(n-1) +(16*n^2 - 76*n + 87)*a(n-2) +3*(4*n^2 - 22*n + 27)*a(n-3) -9*(2*n-5)*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 24 2012 a(n) ~ 3^n * (1 + sqrt(3)/(2*sqrt(Pi*n))). - Vaclav Kotesovec, Jul 02 2015 From Robert Israel, Jun 03 2016: (Start) E.g.f. A(x) satisfies -27 A + (-63 x + 9) A' + (-18 x^2 + 42 x + 39) A'' + (12 x^2 + 68 x - 25) A''' + (16 x^2 - 58 x + 4) A'''' + (-12 x^2 + 11 x) A''''' + 2 x^2 A'''''' = 0. This implies Mathar's conjectured recursion. (End) MAPLE Egf:= exp(3*x)-exp(x)*(1-BesselI(0, 2*x)): S:= series(Egf, x, 101): seq(coeff(S, x, n)*n!, n=0..100); # Robert Israel, Jun 03 2016 MATHEMATICA CoefficientList[Series[E^(3*x)-E^x*(1-BesselI[0, 2*x]), {x, 0, 50}], x] * Range[0, 50]! (* Vaclav Kotesovec, Jul 02 2015 *) CROSSREFS Cf. A025191, A027914, A027915. Sequence in context: A171270 A182879 A124640 * A081250 A135247 A094539 Adjacent sequences:  A081670 A081671 A081672 * A081674 A081675 A081676 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 28 2003 STATUS approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)