The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216860 G.f.: Sum_{n>=0} n!^2 * x^n / Product_{k=1..n} (1 + k*x)^2. 2
 1, 1, 2, 15, 232, 5693, 202398, 9829771, 624964724, 50365047225, 5016187555114, 604968014349767, 86878610741366976, 14648881145458377397, 2865572277481996560950, 643666405504709227632003, 164536267335939429654990988, 47489465018413227906492425009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1 + k*x). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..220 FORMULA a(n) ~ exp(-1) * (n!)^2. - Vaclav Kotesovec, Nov 02 2014 EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 15*x^3 + 232*x^4 + 5693*x^5 + 202398*x^6 +... where A(x) = 1 + x/(1+x)^2 + 2!^2*x^2/((1+x)*(1+2*x))^2 + 3!^2*x^3/((1+x)*(1+2*x)*(1+3*x))^2 + 4!^2*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x))^2 +... PROG (PARI) {a(n)=polcoeff(sum(m=0, n, m!^2*x^m/prod(k=1, m, 1+k*x +x*O(x^n))^2), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A216859. Sequence in context: A197236 A097628 A305111 * A161968 A294043 A326095 Adjacent sequences: A216857 A216858 A216859 * A216861 A216862 A216863 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 17 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 09:50 EST 2023. Contains 367517 sequences. (Running on oeis4.)