A059373 Second diagonal of triangle in A059370.

1, -4, 8, -16, 12, -96, -480, -4672, -45520, -493120, -5798912, -73668608, -1005335552, -14671085568, -228051746304, -3762955404288, -65707303602432, -1210821292674048, -23487031074109440, -478463919131627520, -10214440549929047040, -228069193578011566080

Offset: 2

Author

N. J. A. Sloane, Jan 28 2001

Keywords

• sign
• easy

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 171, #34.

Crossrefs

Cf. A059370.

Programs

Maple

series(RootOf(T*hypergeom([1,2],[],T)-x,T)^2,x=0,21); # Mark van Hoeij, Apr 20 2013

Mathematica

nmax = 23; t[n_, k_] := t[n, k] = Sum[(m+1)!*t[n-m-1, k-1], {m, 0, n-k}]; t[n_, 1] = n!; t[n_, n_] = 1; tnk = Table[t[n, k], {n, 1, nmax}, {k, 1, nmax}]; A059370 = Reverse /@ Inverse[tnk] // DeleteCases[#, 0, 2] & ; Table[A059370[[n, n - 1]], {n, 2, nmax}] (* Jean-François Alcover, Jun 14 2013 *)

PARI

N = 66;  x = 'x + O('x^N);
tf = sum(n=1,N, n!*x^n );
gf=serreverse(%)^2;
v = Vec(gf)
/* Joerg Arndt, Apr 20 2013 */

Formula

G.f. A(x) is (R(x))^2 where R(x) is the series reversion of x*hypergeom([1,2],[],x) = sum(n>=1, n!*x^n), see Comtet. - Mark van Hoeij, Apr 20 2013

Extensions

Added more terms, Mark van Hoeij and Joerg Arndt, Apr 20 2013