A154289 Denominators of coefficients in expansion of 1/ ( Sum_{n>=1} ( x^(n - 1)/(2*n - 1)!! ) ).

1, 3, 45, 945, 14175, 93555, 638512875, 273648375, 44405668125, 194896477400625, 32157918771103125, 201717854109646875, 3028793579456347828125, 698952364489926421875, 564653660170076273671875, 5660878804669082674070015625, 7217620475953080409439269921875

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..100

Formula

G.f.: 1/( Sum_{n>=1}( x^(n - 1)/(2*n - 1)!! ) ) = sqrt(2/Pi) * sqrt(x))/ (exp(x/2) * erf(sqrt(x)/sqrt(2)).

Mathematica

q[x_] = (Sqrt[2/Pi]*Sqrt[x])/ (E^(x/2)*Erf[Sqrt[x]/Sqrt[2]]) ;
Denominator[CoefficientList[Series[q[x], {x, 0, 30}], x]]
(* program improved by Bob Hanlon (hanlonr(AT)cox.net) *)

Prog

(PARI) lista(n) = { n++; x = z + z*O(z^n); P = 1/sum(m=1, n, (x^(m - 1)/prod(k=1, m, 2*k-1))); n--; for (i=0, n, print1(denominator(polcoeff(P, i, z)), ", " ); ); } \\ Michel Marcus, Apr 30 2013
(Sage)
def A154289_list(len):
    R, C = [1], [1]+[0]*(len-1)
    for n in (1..len-1):
        for k in range(n, 0, -1):
            C[k] = C[k-1] / (2*k+1)
        C[0] = -sum(C[k] for k in (1..n))
        R.append((C[0]).denominator())
    return R
print(A154289_list(17)) # Peter Luschny, Feb 21 2016

Crossrefs

Cf. A154288.

Sequence in context: A008931 A036278 A225149 * A171080 A188681 A012827

Adjacent sequences: A154286 A154287 A154288 * A154290 A154291 A154292

Keyword

nonn,frac

Author

Roger L. Bagula, Jan 06 2009

Extensions

Edited by Michel Marcus and Joerg Arndt, Apr 30 2013

Status

approved