A072287 - OEIS

A072287

Let f(n, m) = binomial(n - m/2 + 1, n - m + 1) - binomial(n - m/2, n - m + 1) and let s(n) = Sum_{k=0..n} f(n, k); then a(n) = numerator of s(n).

1, 2, 7, 47, 155, 2027, 6597, 42835, 138875, 3599155, 11654465, 75457289, 244238477, 3161900479, 10232916665, 66231885067, 214336798299, 11097918730051, 35913975952793, 232441522435405, 752199270651129

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OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..1234

FORMULA

s(0)=1, s(1)=2, s(n+1)=s(n)+s(n-1)+binomial(n-1/2, n) for n>=1.

(2*n+3)*s(n) - s(n+1) + (-4*n-7)*s(n+2) + (2*n+4)*s(n+3) = 0. - Robert Israel, Feb 06 2019

EXAMPLE

1,2,7/2,47/8,155/16,2027/128,6597/256,42835/1024,138875/2048,...

MAPLE

S:= gfun:-rectoproc({s(0)=1, s(1)=2, s(2)=7/2, (2*n+3)*s(n) - s(n+1) + (-4*n-7)*s(n+2) + (2*n+4)*s(n+3) = 0, s(n), remember):

map(numer@S, [$0..30]); # Robert Israel, Feb 06 2019

MATHEMATICA

f[n_, m_] := Binomial[n - m/2 + 1, n - m + 1] - Binomial[n - m/2, n - m + 1]; s[n_] := Sum[ f[n, k], {k, 0, n}]; Table [Numerator[s[n]], {n, 0, 26}]

CROSSREFS

Denominator of s(n+1) = A046161(n).

Sequence in context: A116892 A201481 A054555 * A290488 A276649 A091117

Adjacent sequences: A072284 A072285 A072286 * A072288 A072289 A072290

KEYWORD

nonn,easy,frac

AUTHOR

Michele Dondi (bik.mido(AT)tiscalinet.it), Jul 11 2002

STATUS

approved