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 A023880 Number of partitions in expanding space. 9
 1, 1, 5, 32, 298, 3531, 51609, 894834, 17980052, 410817517, 10518031721, 298207687029, 9273094072138, 313757506696967, 11474218056441581, 450961669608632160, 18954582520550896213, 848384721904740036422, 40285256621556957160307, 2022695276960566890383148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also partitions of n into 1 sort of 1, 4 sorts of 2, 27 sorts of 3, ..., k^k sorts of k. - Joerg Arndt, Feb 04 2015 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 FORMULA G.f.: 1 / Product_{k>=1} (1 - x^k)^(k^k). a(n) ~ n^n * (1 + exp(-1)/n + (exp(-1)/2 + 5*exp(-2))/n^2). - Vaclav Kotesovec, Mar 14 2015 a(n) = (1/n)*Sum_{k=1..n} A283498(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 11 2017 MAPLE with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(       add(d*d^d, d=divisors(j)) *a(n-j), j=1..n)/n)     end: seq(a(n), n=0..30);  # Alois P. Heinz, Feb 04 2015 MATHEMATICA nmax=20; CoefficientList[Series[Product[1/(1-x^k)^(k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *) PROG (PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^(k^k))) \\ G. C. Greubel, Oct 31 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^(k^k): k in [1..m]]) )); // G. C. Greubel, Oct 31 2018 CROSSREFS Sequence in context: A305305 A331339 A307497 * A104031 A294957 A023882 Adjacent sequences:  A023877 A023878 A023879 * A023881 A023882 A023883 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)