login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125694 Riordan array ((1+3x-sqrt(1+2x+9x^2))/(2x),(1+3x-sqrt(1+2x+9x^2))/2). 4

%I

%S 1,-2,1,2,-4,1,2,8,-6,1,-10,-4,18,-8,1,6,-24,-26,32,-10,1,42,60,-18,

%T -72,50,-12,1,-102,24,162,48,-150,72,-14,1,-82,-388,-214,248,230,-268,

%U 98,-16,1,782,536,-546,-800,158,600,-434,128,-18,1

%N Riordan array ((1+3x-sqrt(1+2x+9x^2))/(2x),(1+3x-sqrt(1+2x+9x^2))/2).

%C First column is A125695. Row sums are A091593. Inverse of A125693.

%F T(n-1,k-1) = (k/n)*sum_{i=0..n-k} binomial(n,n-k-i) *(-3)^(n-k-i) *binomial(i+n-1,n-1). - Vladimir Kruchinin, Feb 12 2011

%F T(n, k) = (-3)^(n-k)*C(n,k)*hypergeometric([k-n, n+1], [k+2], 1/3). - _Peter Luschny_, Sep 17 2014

%e Triangle begins

%e 1,

%e -2, 1,

%e 2, -4, 1,

%e 2, 8, -6, 1,

%e -10, -4, 18, -8, 1,

%e 6, -24, -26, 32, -10, 1,

%e 42, 60, -18, -72, 50, -12, 1

%t m = 9;

%t T[0, 0] = 1; T[1, 0] = 2; T[1, 1] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = 3 T[n - 1, k] + T[n - 1, k - 1] - T[n - 2, k - 1]; T[_, _] = 0;

%t M = Table[T[n, k], {n, 0, m}, {k, 0, m}] // Inverse;

%t A[n_, k_] := M[[n + 1, k + 1]];

%t Table[A[n, k], {n, 0, m}, {k, 0, n}] // Flatten (* _Jean-Fran├žois Alcover_, Jun 13 2019 *)

%o (Sage)

%o A125694 = lambda n,k : (-3)^(n-k)*binomial(n,k)*hypergeometric([k-n, n+1], [k+2], 1/3)

%o for n in (0..6): [round(A125694(n,k).n(100)) for k in (0..n)] # _Peter Luschny_, Sep 17 2014

%K easy,sign,tabl

%O 0,2

%A _Paul Barry_, Nov 30 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)