This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A155537 Scaled Narayana recursion: m = 0; p = 2; q = 1; a(n,k)=(m*n - m*k + 1)*a(n - 1, k - 1) + (m*k - (m - 1))*a(n - 1, k); f(n) = Product[k + 1, {k, 0, n}]; a0(n,m) = f[n]/(f[m]*f[n - m]); t(n,k)=(p^(n - m)*q^m + p^m*q^(n - m))*a0(n - 1, k - 1)*a(n, k). 0

%I

%S 3,5,5,9,27,9,17,102,102,17,33,330,660,330,33,65,975,3250,3250,975,65,

%T 129,2709,13545,22575,13545,2709,129,257,7196,50372,125930,125930,

%U 50372,7196,257,513,18468,172368,603288,904932,603288,172368,18468,513,1025

%N Scaled Narayana recursion: m = 0; p = 2; q = 1; a(n,k)=(m*n - m*k + 1)*a(n - 1, k - 1) + (m*k - (m - 1))*a(n - 1, k); f(n) = Product[k + 1, {k, 0, n}]; a0(n,m) = f[n]/(f[m]*f[n - m]); t(n,k)=(p^(n - m)*q^m + p^m*q^(n - m))*a0(n - 1, k - 1)*a(n, k).

%C Row sums are:

%C {3, 10, 45, 238, 1386, 8580, 55341, 367510, 2494206, 17215900,...}.

%F m = 0; p = 2; q = 1;

%F a(n,k)=(m*n - m*k + 1)*a(n - 1, k - 1) + (m*k - (m - 1))*a(n - 1, k);

%F f(n) = Product[k + 1, {k, 0, n}];

%F a0(n,m) = f[n]/(f[m]*f[n - m]);

%F t(n,k)=(p^(n - m)*q^m + p^m*q^(n - m))*a0(n - 1, k - 1)*a(n, k).

%e {3},

%e {5, 5},

%e {9, 27, 9},

%e {17, 102, 102, 17},

%e {33, 330, 660, 330, 33},

%e {65, 975, 3250, 3250, 975, 65},

%e {129, 2709, 13545, 22575, 13545, 2709, 129},

%e {257, 7196, 50372, 125930, 125930, 50372, 7196, 257},

%e {513, 18468, 172368, 603288, 904932, 603288, 172368, 18468, 513},

%e {1025, 46125, 553500, 2583000, 5424300, 5424300, 2583000, 553500, 46125, 1025}

%t Clear[A, a0, b0, n, k, m];

%t A[n_, 1, m_] := 1; A[n_, n_, m_] := 1;

%t A[n_, k_, m_] := (m*n - m*k + 1)*A[n - 1, k - 1, m] + (m*k - (m - 1))*A[n - 1, k, m];

%t f[n_] = Product[k + 1, {k, 0, n}]; a0[n_, m_] = f[n]/(f[m]*f[n - m]);;

%t m = 0; p = 2; q = 1;

%t Table[(p^(n - m)*q^m + p^m*q^(n - m))*a0[n - 1, k - 1]*A[n, k, m], {n, 10}, {k, n}];

%t Flatten[%]

%Y A001263

%K nonn,tabl,uned

%O 1,1

%A _Roger L. Bagula_, Jan 23 2009

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.

Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)