The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216367 G.f.: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x)^2. 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 05:27 EST 2020. Contains 338678 sequences. (Running on oeis4.)