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!)
 A355470 Expansion of Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x)^(k+1). 3
 1, 1, 66, 21222, 18927560, 36030104000, 125486684755152, 722272396672485568, 6391048590559497227904, 82362961035803105954736768, 1482370265813455598541301007360, 36031982428595760278113744699088384, 1150873035676373345725887922070318410752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..12. FORMULA E.g.f.: Sum_{k>=0} exp(k^3 * x) * (k^3 * x)^k/k!. a(n) = Sum_{k=0..n} k^(3*n) * binomial(n,k). PROG (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-k^3*x)^(k+1))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp(k^3*x)*(k^3*x)^k/k!))) (PARI) a(n) = sum(k=0, n, k^(3*n)*binomial(n, k)); CROSSREFS Cf. A355469, A355473. Cf. A072034, A242446, A355466. Sequence in context: A282247 A197439 A127706 * A356688 A167778 A199838 Adjacent sequences: A355467 A355468 A355469 * A355471 A355472 A355473 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 03 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 5 20:54 EST 2023. Contains 367594 sequences. (Running on oeis4.)