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

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