OFFSET
0,4
COMMENTS
Self-convolution of A003319. - Vaclav Kotesovec, Aug 03 2015
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 262 (#14).
FORMULA
G.f.: (1-1/Sum (k! x^k ))^2.
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
EXAMPLE
G.f. = x^2 + 2*x^3 + 7*x^4 + 32*x^5 + 177*x^6 + 1142*x^7 + 8411*x^8 + ...
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 01 2001
EXTENSIONS
More terms from Vladeta Jovovic, Mar 04 2001
Prepended a(0)=0, a(1)=0 from Vaclav Kotesovec, Aug 03 2015
STATUS
approved