A113145 Row 4 of table A113143; equal to INVERT of quartic (or 4-fold) factorials shifted one place right.

1, 1, 2, 8, 60, 708, 11428, 232756, 5704964, 163192820, 5331728964, 195776203764, 7978838333188, 357313060904692, 17438518614448580, 921145685670017012, 52355425184381107332, 3185815887918686343924, 206633438251087758833476

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{j=0..k} 4^(k-j)*A111146(k, j).

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A007696(n-k).

G.f.: 1/(T(0) - x) where T(k) = 1 - x*(4*k+1)/(1 - x*(4*k+4)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 19 2013

Example

A(x) = 1 + x + 2*x^2 + 8*x^3 + 60*x^4 + 708*x^5 +...
= 1/(1 - x - x^2 - 5*x^3 - 45*x^4 -...- A007696(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, 4*i+1))); return(polcoeff(A, n, X))}

Crossrefs

Cf. A113143, A007696 (4-fold factorials).

Sequence in context: A355100 A303532 A355106 * A293379 A294331 A036794

Adjacent sequences: A113142 A113143 A113144 * A113146 A113147 A113148

Keyword

nonn

Author

Philippe Deléham and Paul D. Hanna, Oct 28 2005

Status

approved