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A327552 Number of partitions in all twice partitions of n where the first partition is strict. 4
0, 1, 2, 7, 11, 29, 63, 125, 225, 489, 930, 1704, 3260, 5859, 10868, 20026, 35062, 61660, 111789, 191119, 337432, 585847, 1003876, 1705380, 2921394, 4930357, 8311554, 14013583, 23435178, 38849655, 64847870, 106784912, 175699558, 289676875, 472418418, 772944773 (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(3) = 7 = 1+1+1+2+2 counting the partitions in 3, 21, 111, 2|1, 11|1.

MAPLE

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

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

      combinat[numbpart](i)*b(n-i, min(n-i, i-1)))))

    end:

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

seq(a(n), n=0..36);

MATHEMATICA

b[n_, i_] := b[n, i] = If[i(i+1)/2<n, {0, 0}, If[n==0, {1, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i-1]]]]];

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

a /@ Range[0, 36] (* Jean-Fran├žois Alcover, Dec 17 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000009, A000041, A271619, A327607.

Sequence in context: A073602 A057025 A055469 * A336342 A284354 A228076

Adjacent sequences:  A327549 A327550 A327551 * A327553 A327554 A327555

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 16 2019

STATUS

approved

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Last modified January 21 23:44 EST 2022. Contains 350481 sequences. (Running on oeis4.)