A216367 G.f.: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x)^2.

1, 1, 3, 10, 40, 184, 948, 5384, 33300, 222192, 1587512, 12071776, 97206544, 825343600, 7362067888, 68772244640, 670917511424, 6818719677952, 72038876668544, 789610228149632, 8963457852609984, 105211331721594368, 1275095788516589952, 15934546466314258688

Offset

0,3

Comments

Compare to o.g.f. of Bell numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 40*x^4 + 184*x^5 + 948*x^6 +...
where
A(x) = 1 + x/(1-x)^2 + x^2/((1-x)*(1-2*x))^2 + x^3/((1-x)*(1-2*x)*(1-3*x))^2 + x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x))^2 +...

Mathematica

With[{nn=30}, CoefficientList[Series[Sum[x^n/Product[(1-k*x)^2, {k, 0, n}], {n, 0, nn}], {x, 0, nn}], x]] (* Harvey P. Dale, Dec 15 2018 *)

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-k*x +x*O(x^n))^2), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A216373, A000110.

Sequence in context: A300043 A258973 A217885 * A003703 A242651 A231531

Adjacent sequences: A216364 A216365 A216366 * A216368 A216369 A216370

Keyword

nonn

Author

Paul D. Hanna, Sep 05 2012

Status

approved