A059439 A diagonal of A059438.

0, 0, 1, 2, 7, 32, 177, 1142, 8411, 69692, 642581, 6534978, 72754927, 880877928, 11530686953, 162331760494, 2446380427331, 39300220067668, 670480457586813, 12106985274788506, 230691361507912471, 4625811718758963136

Offset: 0

Author

N. J. A. Sloane, Feb 01 2001

Keywords

• nonn
• easy

Comments

Self-convolution of A003319. - Vaclav Kotesovec, Aug 03 2015

Examples

			G.f. = x^2 + 2*x^3 + 7*x^4 + 32*x^5 + 177*x^6 + 1142*x^7 + 8411*x^8 + ...
		

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 262 (#14).

Crossrefs

Cf. A003319, A259472, A260503, A260913.

Programs

Mathematica

a[0]=0; a[n_]:=a[n] = n!-Sum[k!*a[n-k], {k,1,n-1}]; Table[Sum[a[k]*a[n-k],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Aug 03 2015 *)
CoefficientList[Assuming[Element[x, Reals], Series[(1 - x*E^(1/x) / ExpIntegralEi[1/x])^2, {x, 0, 20}]], x] (* Vaclav Kotesovec, Aug 03 2015 *)

Formula

G.f.: (1-1/Sum (k! x^k ))^2.

For n>0, a(n) = A259472(n) + 2*A003319(n). - Vaclav Kotesovec, Aug 03 2015

a(n) ~ 2*(n-1)! * (1 - 1/n - 1/n^2 + 1/n^3 + 30/n^4 + 404/n^5 + 5379/n^6 + 76021/n^7 + 1155805/n^8 + 18931873/n^9 + 333434490/n^10), for coefficients see A260913. - Vaclav Kotesovec, Aug 03 2015

Extensions

More terms from Vladeta Jovovic, Mar 04 2001

Prepended a(0)=0, a(1)=0 from Vaclav Kotesovec, Aug 03 2015