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 A321387 Expansion of Product_{k>=1} (1 + x^k)^(k^(k-1)). 3
 1, 1, 2, 11, 74, 708, 8583, 127424, 2239965, 45514345, 1049365071, 27061132159, 771695223819, 24109698083919, 818914886275467, 30044684789498522, 1184048086192376822, 49883929845112421452, 2237287911899357657492, 106426388125032988691636, 5352033610656721914626572 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Weigh transform of A000169. LINKS N. J. A. Sloane, Transforms FORMULA G.f.: exp(Sum_{k>=1} ( Sum_{d|k} (-1)^(k/d+1)*d^d ) * x^k/k). a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-1)/2 + 2*exp(-2))/n^2). - Vaclav Kotesovec, Nov 09 2018 MAPLE a:=series(mul((1+x^k)^(k^(k-1)), k=1..100), x=0, 21): seq(coeff(a, x, n), n=0..20); # Paolo P. Lava, Apr 02 2019 MATHEMATICA nmax = 20; CoefficientList[Series[Product[(1 + x^k)^(k^(k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d^d, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 20}] PROG (PARI) seq(n)={Vec(exp(sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d^d ) * x^k/k) + O(x*x^n)))} \\ Andrew Howroyd, Nov 09 2018 (PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, (1+x^k)^(k^(k-1)))) \\ G. C. Greubel, Nov 09 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1+x^k)^(k^(k-1)): k in [1..m]]) )); // G. C. Greubel, Nov 09 2018 CROSSREFS Cf. A000169, A023879, A261053, A283335, A321385, A321388. Sequence in context: A212028 A324445 A158265 * A309146 A198088 A112894 Adjacent sequences:  A321384 A321385 A321386 * A321388 A321389 A321390 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 08 2018 STATUS approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)