The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A222524 O.g.f.: Sum_{n>=0} n^n*(2*n+1)^n * exp(-n*(2*n+1)*x) * x^n / n!. 0
 1, 3, 41, 1057, 40057, 2006631, 125093285, 9333786225, 811181004929, 80480710535035, 8975976702322401, 1111688368710017121, 151388120776146737641, 22482576760232188394991, 3616177985990080869347277, 626250139757797928093888481, 116181112230230754285955844865 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..16. FORMULA a(n) = 1/n! * [x^n] Sum_{k>=0} k^k*(2*k+1)^k * x^k / (1 + k*(2*k+1)*x)^(k+1). a(n) = 1/n! * Sum_{k=0..n} (-1)^(n-k)*binomial(n,k) * k^n*(2*k+1)^n. EXAMPLE O.g.f.: A(x) = 1 + 3*x + 41*x^2 + 1057*x^3 + 40057*x^4 + 2006631*x^5 +... where A(x) = 1 + 3*x*exp(-3*x) + 10^2*exp(-10*x)*x^2/2! + 21^3*exp(-21*x)*x^3/3! + 36^4*exp(-36*x)*x^4/4! + 55^5*exp(-55*x)*x^5/5! +... is a power series in x with integer coefficients. PROG (PARI) {a(n)=polcoeff(sum(k=0, n, k^k*(2*k+1)^k*exp(-k*(2*k+1)*x +x*O(x^n))*x^k/k!), n)} for(n=0, 25, print1(a(n), ", ")) (PARI) {a(n)=(1/n!)*polcoeff(sum(k=0, n, k^k*(2*k+1)^k*x^k/(1+k*(2*k+1)*x +x*O(x^n))^(k+1)), n)} for(n=0, 20, print1(a(n), ", ")) (PARI) {a(n)=1/n!*sum(k=0, n, (-1)^(n-k)*binomial(n, k)*k^n*(2*k+1)^n)} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A217900, A217901. Sequence in context: A300281 A012175 A007313 * A241704 A181675 A012053 Adjacent sequences: A222521 A222522 A222523 * A222525 A222526 A222527 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 24 2013 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 June 15 02:34 EDT 2024. Contains 373402 sequences. (Running on oeis4.)