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A050315 Main diagonal of A050314. 23
1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 2, 5, 2, 5, 5, 15, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15, 15, 52, 5, 15, 15, 52, 15, 52, 52, 203, 1, 2, 2, 5, 2, 5, 5, 15, 2, 5, 5, 15, 5, 15, 15, 52, 2, 5, 5, 15, 5, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Also, a(n) is the number of odd multinomial coefficients n!/(k_1!...k_m!) with 1 <= k_1 <= ... <= k_m and k_1 + ... + k_m = n. - Pontus von Brömssen, Mar 23 2018
From Gus Wiseman, Mar 30 2019: (Start)
Also the number of strict integer partitions of n with no binary carries. The Heinz numbers of these partitions are given by A325100. A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion. For example, the a(1) = 1 through a(15) = 15 strict integer partitions with no binary carries are:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C) (D) (E) (F)
(21) (41) (42) (43) (81) (82) (83) (84) (85) (86) (87)
(52) (92) (94) (A4) (96)
(61) (A1) (C1) (C2) (A5)
(421) (821) (841) (842) (B4)
(C3)
(D2)
(E1)
(843)
(852)
(861)
(942)
(A41)
(C21)
(8421)
(End)
LINKS
FORMULA
Bell number of number of 1's in binary: a(n) = A000110(A000120(n)).
MAPLE
a:= n-> combinat[bell](add(i, i=convert(n, base, 2))):
seq(a(n), n=0..100); # Alois P. Heinz, Apr 08 2019
MATHEMATICA
binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]], {n, 0, 20}] (* Gus Wiseman, Mar 30 2019 *)
a[n_] := BellB[DigitCount[n, 2, 1]];
a /@ Range[0, 100] (* Jean-François Alcover, May 21 2021 *)
CROSSREFS
Main diagonal of A307431 and of A307505.
Sequence in context: A208888 A258783 A079318 * A128978 A325110 A357888
KEYWORD
nonn
AUTHOR
Christian G. Bower, Sep 15 1999
STATUS
approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)