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A059439 A diagonal of A059438. 5
0, 0, 1, 2, 7, 32, 177, 1142, 8411, 69692, 642581, 6534978, 72754927, 880877928, 11530686953, 162331760494, 2446380427331, 39300220067668, 670480457586813, 12106985274788506, 230691361507912471, 4625811718758963136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=0..21.

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

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

Cf. A003319, A259472, A260503, A260913.

Sequence in context: A125223 A277359 A005362 * A190123 A006014 A121555

Adjacent sequences:  A059436 A059437 A059438 * A059440 A059441 A059442

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

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Last modified November 20 14:53 EST 2018. Contains 317402 sequences. (Running on oeis4.)