A144506 Column 3 of triangle in A144505, negated.

0, 0, 0, 0, 1, 14, 175, 2330, 34300, 561386, 10179309, 203240850, 4439192835, 105413331100, 2705921548616, 74703337429084, 2207904948683525, 69575538504102190, 2329022305536291275, 82546355086989894366, 3088417981826529182964, 121651432581579519835950, 5032424258902838518567945

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Formula

a(n) = Sum_{k=0..n-4} (n+k-1)!/(6*k!*(n-k-4)!*2^k).

a(n) = ( (n-3)*(4*n^2 - 24*n + 41)*a(n-1) + (n-2)*(2*n-5)*a(n-2) )/((n-4)*(2*n-7)), with a(0)=a(1)=a(2)=a(3)= 0, and a(4) = 1. - G. C. Greubel, Oct 10 2023

Maple

f3:=proc(n) local k; add((n+k-1)!/(6*(n-k-4)!*k!*2^k), k=0..n-4); end;
[seq(f3(n), n=0..60)];

Mathematica

a[n_]:= a[n]= If[n<4, 0, If[n==4, 1, ((n-3)*(4*n^2-24*n+41)*a[n-1] + (n -2)*(2*n-5)*a[n-2])/((n-4)*(2*n-7))]]; (* a = A144506 *)
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 10 2023 *)

Prog

(Magma) I:=[0, 0, 0, 0, 1]; [n le 5 select I[n] else ((n-4)*(4*n^2-32*n+69)*Self(n-1) + (n-3)*(2*n-7)*Self(n-2))/((n-5)*(2*n-9)): n in [1..30]]; // A144506 // G. C. Greubel, Oct 10 2023
(SageMath)
@CachedFunction
def A144506(n): return sum(binomial(n-4, j)*rising_factorial(n-3, j+3)/(6*2^j) for j in range(n-3))
[A144506(n) for n in range(31)] # G. C. Greubel, Oct 10 2023

Crossrefs

Sequence in context: A269680 A269469 A349858 * A177072 A274565 A125471

Adjacent sequences: A144503 A144504 A144505 * A144507 A144508 A144509

Keyword

nonn

Author

N. J. A. Sloane, Dec 14 2008

Status

approved