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 60th year, we have over 367,000 sequences, and we’ve reached 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!)
 A351282 a(n) = Sum_{k=0..n} 3^k * k^(n-k). 2
 1, 3, 12, 48, 201, 885, 4116, 20298, 106365, 592455, 3503532, 21946620, 145210305, 1011726417, 7400390052, 56668826118, 453116188821, 3774297532467, 32682069679548, 293632972911048, 2732593851548985, 26299137526992525, 261387306941467188, 2679392140776188706 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..572 FORMULA a(n) ~ sqrt(2*Pi/(1 + LambertW(exp(1)*n/3))) * n^(n + 1/2) * exp(n/LambertW(exp(1)*n/3) - n) / LambertW(exp(1)*n/3)^(n + 1/2). G.f.: Sum_{k>=0} 3^k * x^k / (1 - k*x). - Ilya Gutkovskiy, Feb 06 2022 MATHEMATICA Join[{1}, Table[Sum[3^k*k^(n-k), {k, 0, n}], {n, 1, 25}]] PROG (PARI) a(n) = sum(k=0, n, 3^k*k^(n-k)); \\ Michel Marcus, Feb 06 2022 CROSSREFS Cf. A003101, A351279. Sequence in context: A103943 A283679 A165328 * A142873 A301578 A151168 Adjacent sequences: A351279 A351280 A351281 * A351283 A351284 A351285 KEYWORD nonn AUTHOR Vaclav Kotesovec, Feb 06 2022 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 9 13:48 EST 2023. Contains 367691 sequences. (Running on oeis4.)