OFFSET
0,2
COMMENTS
Hankel transform is 7^C(n+1,2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} A120730(n,k) * 7^k.
a(n) = ( 8*(n+1)*a(n-1) + 28*(n-2)*a(n-2) - 224*(n-2)*a(n-3) )/(n+1). - G. C. Greubel, Nov 09 2022
MATHEMATICA
a[n_]:= a[n]= If[n==0, 1, If[OddQ[n], 8*a[n-1] -7^((n-1)/2)*CatalanNumber[(n-1)/2], 8*a[n-1]]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Nov 09 2022 *)
PROG
(Magma) [n le 3 select Factorial(n+5)/720 else (8*n*Self(n-1) + 28*(n-3)*Self(n-2) - 224*(n-3)*Self(n-3))/n: n in [1..30]]; // G. C. Greubel, Nov 09 2022
(SageMath)
def a(n): # a = A156362
if (n==0): return 1
elif (n%2==1): return 8*a(n-1) - 7^((n-1)/2)*catalan_number((n-1)/2)
else: return 8*a(n-1)
[a(n) for n in (0..30)] # G. C. Greubel, Nov 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Feb 08 2009
STATUS
approved