The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A162649 E.g.f. satisfies: A(x) = exp( x*cosh(x*A(x)) ). 2
 1, 1, 1, 4, 37, 276, 2221, 26888, 397097, 6055696, 103023481, 2047621632, 44856857101, 1051415079872, 26792169643877, 743266588537216, 22085066412427729, 698048232173484288, 23495515539312273265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..300 FORMULA a(n) = Sum_{k=0..n} C(n,k)*(n-k+1)^(k-1)*Sum_{j=0..k} C(k,j)*(2j-k)^(n-k)/2^k. Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n!, then a(n,m) = Sum_{k=0..n} C(n,k)*m*(n-k+m)^(k-1)*Sum_{j=0..k} C(k,j)*(2j-k)^(n-k)/2^k. a(n) ~ sqrt((s*(r*s+sqrt(1+r^4*s^2))) / (r*(1+r*s*sqrt(1+r^4*s^2)))) * n^(n-1) / (exp(n)*r^n), where r = 0.49285491893166753586122556276745..., s = 2.549795671338977846249694869195317... are roots of the system of equations r*cosh(r*s) = log(s), r^2*sinh(r*s) = 1/s. - Vaclav Kotesovec, Jul 14 2014 EXAMPLE E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 37*x^4/4! + 276*x^5/5! +... log(A(x)) = x*cosh(A(x)) where cosh(A(x)) = 1 + x^2/2! + 6*x^3/3! + 25*x^4/4! + 160*x^5/5! + 1921*x^6/6! +... PROG (PARI) {a(n, m=1)=sum(k=0, n, binomial(n, k)*m*(n-k+m)^(k-1)*sum(j=0, k, binomial(k, j)*(2*j-k)^(n-k)/2^k))} CROSSREFS Sequence in context: A335773 A201865 A025542 * A221059 A197966 A199690 Adjacent sequences:  A162646 A162647 A162648 * A162650 A162651 A162652 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 08 2009 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 December 3 18:19 EST 2021. Contains 349467 sequences. (Running on oeis4.)