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A327590 Number of partitions in all twice partitions of n. 2
0, 1, 4, 10, 29, 63, 164, 339, 797, 1640, 3578, 7139, 15210, 29621, 60381, 117116, 232523, 442388, 863069, 1621560, 3105993, 5785525, 10894394, 20083143, 37434186, 68344449, 125774280, 228088127, 415668548, 747660318, 1351364816, 2413792653, 4327245170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

EXAMPLE

a(3) = 10 = 1+1+1+2+2+3 counting the partitions in 3, 21, 111, 2|1, 11|1, 1|1|1.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0, b(n, i-1)+

      (p-> p+[0, p[1]])(combinat[numbpart](i)*b(n-i, min(n-i, i)))))

    end:

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

seq(a(n), n=0..42);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i]]]]];

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

a /@ Range[0, 42] (* Jean-Fran├žois Alcover, Dec 16 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000041, A006128, A063834, A066633, A327552, A327553, A327554, A327594.

Sequence in context: A164361 A006907 A305204 * A321344 A329156 A052946

Adjacent sequences:  A327587 A327588 A327589 * A327591 A327592 A327593

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2019

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)