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 A331517 a(n) = Sum_{k=0..n} p(n,k) * !k, where p(n,k) = number of partitions of n into k parts and !k = subfactorial of k. 3
 1, 0, 1, 3, 13, 59, 336, 2245, 17408, 153124, 1505420, 16342711, 194060616, 2501178199, 34766184181, 518332353130, 8250146291076, 139618375340912, 2503167665128431, 47393482639721484, 944910760664087791, 19787603213440946946, 434229133448518143203 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..400 FORMULA G.f.: Sum_{k>=0} !k * x^k / Product_{j=1..k} (1 - x^j). a(n) ~ exp(-1) * n! * (1 + 1/n + 2/n^2 + 5/n^3 + 16/n^4 + 60/n^5 + 253/n^6 + 1180/n^7 + 6023/n^8 + 33306/n^9 + 197719/n^10 + ...), for coefficients see A331826. - Vaclav Kotesovec, Jan 28 2020 MATHEMATICA Table[Sum[Length[IntegerPartitions[n, {k}]] Subfactorial[k], {k, 0, n}], {n, 0, 22}] nmax = 22; CoefficientList[Series[Sum[Subfactorial[k] x^k/Product[(1 - x^j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A000166, A008284, A101880, A331518. Sequence in context: A330799 A317776 A145942 * A074437 A026578 A199641 Adjacent sequences:  A331514 A331515 A331516 * A331518 A331519 A331520 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 19 2020 STATUS approved

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Last modified April 8 21:44 EDT 2020. Contains 333329 sequences. (Running on oeis4.)