A113149 Row 8 of table A113143; equal to INVERT of 8-fold factorials shifted one place right.

1, 1, 2, 12, 176, 4184, 134824, 5451528, 264710536, 14992543432, 969925065992, 70547721068232, 5697913588192520, 505926926171909576, 48979597517592503560, 5134435963996172979912, 579379155027833982679816

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = Sum_{j=0..k} 8^(k-j)*A111146(k, j).

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A045755(n-k).

Example

A(x) = 1 + x + 2*x^2 + 12*x^3 + 176*x^4 + 4184*x^5 +...
= 1/(1 - x - x^2 - 9*x^3 - 153*x^4 -...- A045755(n)*x^(n+1)
-...).

Prog

(PARI) {a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0, n, x^j*prod(i=0, j, 8*i+1))); return(polcoeff(A, n, X))}

Crossrefs

Cf. A113143, A045755 (8-fold factorials).

Sequence in context: A231085 A059522 A271857 * A156143 A007129 A125861

Adjacent sequences: A113146 A113147 A113148 * A113150 A113151 A113152

Keyword

nonn

Author

Philippe Deléham and Paul D. Hanna, Oct 28 2005

Status

approved