A113144 Row 3 of table A113143; equal to INVERT of triple (or 3-fold) factorials shifted one place right.

1, 1, 2, 7, 41, 364, 4409, 67573, 1248626, 26948347, 664414997, 18409263772, 566018365445, 19117946453041, 703533848468330, 28013710891743007, 1199943043040160401, 55013996422974758476, 2687888298887895948065, 139414898768304344206141

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{j=0..k} 3^(k-j)*A111146(k, j).

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A007559(n-k).

G.f.: 1/(Q(0)-x) where Q(k) = 1 - x*(3*k+1)/( 1 - x*(3*k+3)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 21 2013

Example

A(x) = 1 + x + 2*x^2 + 7*x^3 + 41*x^4 + 364*x^5 + 4409*x^6
+...
= 1/(1 - x - x^2 - 4*x^3 - 28*x^4 -...- A007559(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, 3*i+1))); return(polcoeff(A, n, X))}

Crossrefs

Cf. A113143, A007559 (3-fold factorials).

Sequence in context: A006677 A346271 A101390 * A320415 A006846 A047864

Adjacent sequences: A113141 A113142 A113143 * A113145 A113146 A113147

Keyword

nonn

Author

Philippe Deléham and Paul D. Hanna, Oct 28 2005

Status

approved