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 A327594 Number of parts in all twice partitions of n. 6
 0, 1, 5, 14, 44, 100, 274, 581, 1417, 2978, 6660, 13510, 29479, 58087, 120478, 236850, 476913, 916940, 1812498, 3437043, 6657656, 12512273, 23780682, 44194499, 83117200, 152837210, 283431014, 517571202, 949844843, 1719175176, 3127751062, 5618969956, 10133425489 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..3200 EXAMPLE a(2) = 5 = 1+2+2 counting the parts in 2, 11, 1|1. a(3) = 14 = 1+2+3+2+3+3: 3, 21, 111, 2|1, 11|1, 1|1|1. MAPLE g:= proc(n) option remember; (p-> [p(n), add(p(n-j)*       numtheory[tau](j), j=1..n)])(combinat[numbpart])     end: b:= proc(n, i) option remember; `if`(n=0, [1, 0],       `if`(i<2, 0, b(n, i-1)) +(h-> (f-> f +[0, f[1]*        h[2]/h[1]])(b(n-i, min(n-i, i))*h[1]))(g(i)))     end: a:= n-> b(n\$2)[2]: seq(a(n), n=0..37); # second Maple program: b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],      `if`(k=0, [1, 1], `if`(i<2, 0, b(n, i-1, k))+          (h-> (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*         b(n-i, min(n-i, i), k)))(b(i\$2, k-1))))     end: a:= n-> b(n\$2, 2)[2]: seq(a(n), n=0..37); MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[k == 0, {1, 1}, If[i < 2, 0, b[n, i - 1, k]] + Function[h, Function[f, f + {0, f[[1]] h[[2]]/ h[[1]]}][h[[1]] b[n - i, Min[n - i, i], k]]][b[i, i, k - 1]]]]; a[n_] := b[n, n, 2][[2]]; a /@ Range[0, 37] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *) CROSSREFS Cf. A000041, A006128, A063834, A327590, A327605, A327607, A327608. Column k=2 of A327618. Sequence in context: A120901 A222988 A349222 * A034530 A125246 A302762 Adjacent sequences:  A327591 A327592 A327593 * A327595 A327596 A327597 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 18 2019 STATUS approved

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Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)