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 A300489 a(n) = n! * [x^n] -log(1 - x)/(1 - n*x). 1
 0, 1, 5, 65, 1766, 83674, 6124584, 639826452, 90328291248, 16558780949136, 3823322392154880, 1085461798576638240, 371610484248792556800, 150961314165968542273920, 71790302154674639506682880, 39506878580692178250399571200, 24909116615180033772524150937600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = n!*n^n*Sum_{k=1..n} 1/(k*n^k). EXAMPLE The table of coefficients of x^k in expansion of e.g.f. -log(1 - x)/(1 - n*x) begins: n = 0: (0), 1, 1, 2, 6, 24, ... n = 1: 0, (1), 3, 11, 50, 274, ... n = 2: 0, 1, (5), 32, 262, 2644, ... n = 3: 0, 1, 7, (65), 786, 11814, ... n = 4: 0, 1, 9, 110, (1766), 35344, ... n = 5: 0, 1, 11, 167, 3346, (83674), ... ... This sequence is the main diagonal of the table. MATHEMATICA Table[n! SeriesCoefficient[-Log[1 - x]/(1 - n x), {x, 0, n}], {n, 0, 16}] Join[{0}, Table[n! n^n Sum[1/(k n^k), {k, 1, n}], {n, 1, 16}]] PROG (PARI) a(n) = n!*n^n*sum(i=1, n, 1/(i*n^i)); \\ Altug Alkan, Mar 08 2018 CROSSREFS Cf. A000254, A068102, A069015, A104150. Sequence in context: A218221 A046881 A336674 * A214348 A195196 A012635 Adjacent sequences: A300486 A300487 A300488 * A300490 A300491 A300492 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 07 2018 STATUS approved

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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)