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!)
 A299786 Expansion of Product_{k>=1} (1 + k^(k-1)*x^k). 2
 1, 1, 2, 11, 73, 707, 8547, 127379, 2237804, 45511484, 1049155214, 27060763974, 771662014455, 24109614539775, 818906748562249, 30044648617150066, 1184045057676213763, 49883902402848781573, 2237286132689496359239, 106426356238092171308928, 5352031894869594850387969 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1, g(n) = (-1) * n^(n-1). - Seiichi Manyama, Aug 22 2020 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..387 FORMULA a(n) ~ n^(n-1) * (1 + exp(-1)/n + (2*exp(-2) + 3*exp(-1)/2)/n^2). - Vaclav Kotesovec, Jan 22 2019 MATHEMATICA nmax = 20; CoefficientList[Series[Product[(1 + k^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d^(k - k/d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 20}] PROG (PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1+k^(k-1)*x^k)) \\ Seiichi Manyama, Aug 22 2020 CROSSREFS Cf. A265949, A266964, A304961, A321387, A323634. Sequence in context: A323842 A049671 A074609 * A335310 A199417 A114179 Adjacent sequences: A299783 A299784 A299785 * A299787 A299788 A299789 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 21 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 01:49 EST 2023. Contains 367616 sequences. (Running on oeis4.)