A368502 -id:A368502 - cp's OEIS frontend

A368503 Number of partitions of an n-set into blocks of size <= n/2.

1, 0, 1, 1, 10, 26, 166, 652, 3795, 18755, 112124, 648649, 4163743, 27216840, 190168577, 1376119903, 10468226150, 82744297014, 681863474058, 5830425411936, 51720008131148, 474821737584174, 4506628734688128, 44150936144057758, 445956917001833090, 4638564968368158592

Offset: 0

Ilya Gutkovskiy, Dec 27 2023

nonn

Cf. A000110, A110618, A368502.

Table[n! SeriesCoefficient[Exp[Sum[x^j/j!, {j, 1, Floor[n/2]}]], {x, 0, n}], {n, 0, 25}]

a(n) = n! * [x^n] exp( Sum_{1 <= j <= n/2} x^j / j! ).

A368511 Number of ordered partitions of an n-set into blocks of size <= sqrt(n).

Original entry on oeis.org

1, 1, 2, 6, 66, 450, 3690, 35280, 385560, 6717480, 96117000, 1512819000, 25975395600, 483169486800, 9678799930800, 207733600074000, 5243385642495000, 128458209887007000, 3332234177825553000, 91241046790816923000, 2629791992312269785000, 79586945507310941700000

Offset: 0

Ilya Gutkovskiy, Dec 28 2023

nonn

Cf. A000670, A368502, A368512.

Table[n! SeriesCoefficient[1/(1 - Sum[x^j/j!, {j, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 21}]

a(n) = n! * [x^n] 1 / (1 - Sum_{1 <= j <= sqrt(n)} x^j / j!).

cp's OEIS Frontend

A368503 Number of partitions of an n-set into blocks of size <= n/2.

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