# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a317912 Showing 1-1 of 1 %I A317912 #10 Dec 08 2020 11:40:33 %S A317912 1,0,2,3,8,11,31,41,101,156,318,498,1037,1555,3024,4889,8849,14112, %T A317912 25622,40322,71314,113926,194677,310819,530030,835484,1400523,2226307, %U A317912 3668998,5797558,9521310,14942262,24298136,38187102,61384028,96161997,154078991,239891926,381723396 %N A317912 Expansion of Product_{k>=2} 1/(1 - k*x^k). %C A317912 First differences of A006906. %C A317912 Sum of products of terms in all partitions of n into parts >= 2. %H A317912 Seiichi Manyama, Table of n, a(n) for n = 0..5000 %H A317912 Index entries for sequences related to partitions %F A317912 G.f.: exp(Sum_{j>=1} Sum_{k>=2} k^j*x^(j*k)/j). %e A317912 a(6) = 31 because we have [6], [4, 2], [3, 3], [2, 2, 2] and 6 + 4*2 + 3*3 + 2*2*2 = 31. %p A317912 b:= proc(n, i) option remember; `if`(n=0 or i=1, 1, %p A317912 b(n, i-1)+ i*b(n-i, min(n-i, i))) %p A317912 end: %p A317912 a:= n-> b(n$2) -`if`(n=0, 0, b(n-1$2)): %p A317912 seq(a(n), n=0..40); # _Alois P. Heinz_, Aug 10 2018 %t A317912 nmax = 38; CoefficientList[Series[Product[1/(1 - k x^k), {k, 2, nmax}], {x, 0, nmax}], x] %t A317912 nmax = 38; CoefficientList[Series[Exp[Sum[Sum[k^j x^(j k)/j, {k, 2, nmax}], {j, 1, nmax}]], {x, 0, nmax}], x] %t A317912 b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d^(k/d + 1), {d, Divisors[k]}] b[n - k], {k, 1, n}]/n]; Differences[Table[b[n], {n, -1, 38}]] %Y A317912 Cf. A002865, A006906, A191659, A302830. %K A317912 nonn %O A317912 0,3 %A A317912 _Ilya Gutkovskiy_, Aug 10 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE