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A099252 Bisection of A005043. 3
0, 1, 6, 36, 232, 1585, 11298, 83097, 625992, 4805595, 37458330, 295673994, 2358641376, 18985057351, 154000562758, 1257643249140, 10331450919456, 85317692667643, 707854577312178, 5897493615536452, 49320944483427000, 413887836110423787, 3484084625456932134, 29412628894558563849 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

G. F. Smith, Title?, Tensor, Vol. 19 (1968), p. 79.

LINKS

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

D. L. Andrews, Letter to N. J. A. Sloane, Apr 10 1978.

FORMULA

Recurrence: (n+1)*(2*n+1)*a(n) = n*(26*n-7)*a(n-1) - 3*(26*n^2 - 61*n + 39)*a(n-2) + 27*(n-2)*(2*n-3)*a(n-3). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 3^(2*n+5/2)/(16*sqrt(2*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 17 2012

MAPLE

G:=(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)): Gser:=series(G, x=0, 60): seq(coeff(Gser, x^(2*n-1)), n=1..25); # Emeric Deutsch

MATHEMATICA

Take[CoefficientList[Series[(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x)), {x, 0, 60}], x], {2, -1, 2}] (* Vaclav Kotesovec, Oct 17 2012 *)

PROG

(PARI) x='x+O('x^66); v=Vec((1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x))); vector(#v\2, n, v[2*n]) \\ Joerg Arndt, May 12 2013

(Sage)

def A():

    a, b, c, d, n = 0, 1, 1, -1, 1

    yield 0

    while True:

        n += 1

        a, b = b, (3*(n-1)*n*a+(2*n-1)*n*b)//((n+1)*(n-1))

        c, d = d, (3*(n-1)*c-(2*n-1)*d)//n

        if n%2: yield -(d + b)*(1-(-1)^n)//2

A099252  = A()

print([A099252 .next() for _ in range(24)]) # Peter Luschny, May 16 2016

CROSSREFS

Cf. A005043, A099251.

Sequence in context: A244889 A144819 A284647 * A057395 A259819 A213282

Adjacent sequences:  A099249 A099250 A099251 * A099253 A099254 A099255

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 16 2004

EXTENSIONS

More terms from Emeric Deutsch, Nov 18 2004

STATUS

approved

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Last modified February 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)