This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A305562 Coefficients associated with power series solution of g'(x) = g(x/2) e^x at x=0. 0
 1, 1, 3, 19, 251, 6843, 381851, 43357211, 9976746651, 4639483488923, 4351708606681243, 8221479626141796507, 31252321079882850259099, 238835886863534101328335003, 3667031594654877566958673359003, 113055325655546855868908521812586651 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The series g(x) := Sum_{n>=0} a(n) * 2^((-n*n+n)/2) * x^n / n! satisfies g'(x) = g(x/2) e^x. The denominators of the power series can be found at A006125. - Lewis Chen, Apr 28 2019 LINKS FiveThirtyEight, The Riddler (Apr. 26, 2019) (Riddler Express), with solution FORMULA a(n+1) = Sum_{n=0..k} a(k)*binomial(n, k)*2^( (n*n+n - k*k-k)/2 ). PROG (PARI) {a(n) = if( n<1, n==0, n--; sum(k=0, n, a(k) * binomial(n, k) * 2^( (n*n+n - k*k-k)/2 )))}; CROSSREFS Cf. A006125. Sequence in context: A054590 A261495 A069344 * A316294 A233240 A173799 Adjacent sequences:  A305559 A305560 A305561 * A305563 A305564 A305565 KEYWORD nonn,frac AUTHOR Michael Somos, Jun 04 2018 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 August 21 23:04 EDT 2019. Contains 326169 sequences. (Running on oeis4.)