A144507 Column 4 of triangle in A144505.

0, 0, 0, 0, 0, 1, 20, 330, 5495, 97405, 1867446, 38849790, 875734035, 21320230140, 558453090910, 15677076200786, 469894617088260, 14985440023696415, 506831098757070010, 18125347345533260190, 683518670893880841921, 27112243165544881804755, 1128576366359460556636770

Offset

0,7

Links

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

Formula

a(n) = (1/4!)*Sum_{k=0..n-5} (n+k-1)!/((n-k-5)!*k!*2^k).

a(n) = A001516(n-3)/6 for n > 2. [Corrected by Georg Fischer, Jan 25 2020]

a(n) = ( (2*n-7)*(n^2 -7*n +14)*a(n-1) + (n-2)*(n-3)*a(n-2) )/((n-4)*(n-5)), with a(0)=a(1)=a(2)=a(3)=a(4)=0, and a(5)=1. - G. C. Greubel, Oct 10 2023

Maple

f4:=proc(n) local k; add((n+k-1)!/(4!*(n-k-5)!*k!*2^k), k=0..n-5); end;
[seq(f4(n), n=0..60)];

Mathematica

Table[Sum[1/6 (n+k+2)!/(2^(k+2) (n-k-2)! k!), {k, 0, n-2}], {n, -3, 20}] (* Vincenzo Librandi, Jan 27 2020 *)

Prog

(Magma) I:=[0, 0, 0, 0, 0, 1]; [n le 6 select I[n] else ((2*n-9)*(n^2-9*n+22)*Self(n-1) + (n-3)*(n-4)*Self(n-2))/((n-5)*(n-6)): n in [1..32]]; // G. C. Greubel, Oct 10 2023
(SageMath)
@CachedFunction
def A144507(n): return sum(binomial(n-5, j)*rising_factorial(n-4, j+4)/(24*2^j) for j in range(n-4))
[A144507(n) for n in range(31)] # G. C. Greubel, Oct 10 2023

Crossrefs

Cf. A001516, A144505, A144506.

Sequence in context: A304723 A273590 A187512 * A084032 A166984 A167031

Adjacent sequences: A144504 A144505 A144506 * A144508 A144509 A144510

Keyword

nonn

Author

N. J. A. Sloane, Dec 14 2008

Status

approved