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!)
 A328182 Expansion of e.g.f. 1 / (2 - exp(3*x)). 3
 1, 3, 27, 351, 6075, 131463, 3413907, 103429791, 3581223435, 139498558263, 6037616347587, 287444492409231, 14929010774254395, 839982382565841063, 50897213545996785267, 3304312091004451756671, 228821504027595115886955, 16836102104577636004291863, 1311625494765417347634022947 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(0) = 1; a(n) = Sum_{k=1..n} 3^k * binomial(n,k) * a(n-k). a(n) = Sum_{k>=0} (3*k)^n / 2^(k + 1). a(n) = 3^n * A000670(n). a(n) ~ n! * 3^n / (2 * log(2)^(n+1)). - Vaclav Kotesovec, Aug 09 2021 MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(       a(n-j)*binomial(n, j)*3^j, j=1..n))     end: seq(a(n), n=0..20);  # Alois P. Heinz, Oct 06 2019 MATHEMATICA nmax = 18; CoefficientList[Series[1/(2 - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]! a[0] = 1; a[n_] := a[n] = Sum[3^k Binomial[n, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}] Table[3^n HurwitzLerchPhi[1/2, -n, 0]/2, {n, 0, 18}] CROSSREFS Cf. A000670, A216794, A247452, A328183. Sequence in context: A067000 A307650 A168593 * A157089 A138436 A141057 Adjacent sequences:  A328179 A328180 A328181 * A328183 A328184 A328185 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Oct 06 2019 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 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)