1,1

Each partition of n, ordered like in Abramowitz-Stegun (A-St order; for the reference see A134278), is mapped to 1 if the partition has parts 1 or 2 only and to 0 otherwise.

First member (K=1) in the family M31hat(-K) of partition number arrays.

The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].

This array is array A144357 divided entrywise by the array M_3=M3(1)=A036040. Formally 'A144357/A036040'. E.g. a(4,3)= 1 = 3/3 = A144357(4,3)/A036040(4,3).

If M31hat(-1;n,k) is summed over those k numerating partitions with fixed number of parts m one obtains the unsigned triangle S1hat(-1):= A145362 .

W.Lang, Combinatorial Interpretation of Generalized Stirling Numbers, preprint Oct 2008.

W. Lang, First 10 rows of the array and more.

a(n,k) = product(S1(-1;j,1)^e(n,k,j),j=1..n) with S1(-1;n,1) = A008279(1,n-1) = [1,1,0,0,0,...], n>=1 and the exponent e(n,k,j) of j in the k-th partition of n in the A-St ordering of the partitions of n.

[1];[1,1];[0,1,1];[0,0,1,1,1];[0,0,0,0,1,1,1];...

a(4,3)= 1 = S1(-1;2,1)^2. The relevant partition of 4 is (2^2).

A145363 (M31hat(-2)).

Sequence in context: A085357 A132971 A011748 this_sequence A130304 A118274 A080909

Adjacent sequences: A145358 A145359 A145360 this_sequence A145362 A145363 A145364

nonn,easy,tabf

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 17 2008

In %N: changed 'partition' to 'partitions'.In the last %C line: after 'k' added 'numerating partitions'. - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 17 2008