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A327607 Number of parts in all twice partitions of n where the first partition is strict. 6
0, 1, 3, 11, 21, 58, 128, 276, 516, 1169, 2227, 4324, 8335, 15574, 29116, 55048, 97698, 176291, 323277, 563453, 1005089, 1770789, 3076868, 5293907, 9184885, 15668638, 26751095, 45517048, 76882920, 128738414, 217219751, 360525590, 599158211, 995474365 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..4000

EXAMPLE

a(3) = 11 = 1+2+3+2+3 counting the parts in 3, 21, 111, 2|1, 11|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`(i*(i+1)/2<n, 0,

`if`(n=0, [1, 0], b(n, i-1) +(h-> (f-> f+[0, f[1]*

h[2]/h[1]])(b(n-i, min(n-i, i-1))*h[1]))(g(i))))

end:

a:= n-> b(n$2)[2]:

seq(a(n), n=0..37);

MATHEMATICA

g[n_] := g[n] = {PartitionsP[n], Sum[PartitionsP[n - j] DivisorSigma[0, j], {j, 1, n}]};

b[n_, i_] := b[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, {1, 0}, Module[{h, f}, h = g[i]; f = b[n - i, Min[n - i, i - 1]] h[[1]]; b[n, i - 1] + f + {0, f[[1]] h[[2]] / h[[1]]}]]];

a[n_] := b[n, n][[2]];

a /@ Range[0, 37] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000009, A000041, A271619, A327552, A327594, A327605, A327608.

Sequence in context: A064568 A147073 A147191 * A034185 A184053 A240371

Adjacent sequences: A327604 A327605 A327606 * A327608 A327609 A327610

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2019

STATUS

approved

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Last modified December 9 12:54 EST 2022. Contains 358700 sequences. (Running on oeis4.)