A156362 a(2*n+2) = 8*a(2*n+1), a(2*n+1) = 8*a(2*n) - 7^n*A000108(n), a(0)=1.

1, 7, 56, 441, 3528, 28126, 225008, 1798349, 14386792, 115060722, 920485776, 7363180314, 58905442512, 471228010428, 3769824083424, 30158239367445, 241265914939560, 1930119075851050, 15440952606808400, 123527424655229966

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

Cf. A000108, A001405, A151162, A156195, A151254, A151281, A156266, A156361.

Sequence in context: A229248 A242159 A057090 * A055274 A152776 A155197

Adjacent sequences: A156359 A156360 A156361 * A156363 A156364 A156365

Keyword

nonn

Author

Philippe Deléham, Feb 08 2009

Status

approved