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 A144885 Partition number array, called M31hat(4). 4
 1, 4, 1, 20, 4, 1, 120, 20, 16, 4, 1, 840, 120, 80, 20, 16, 4, 1, 6720, 840, 480, 400, 120, 80, 64, 20, 16, 4, 1, 60480, 6720, 3360, 2400, 840, 480, 400, 320, 120, 80, 64, 20, 16, 4, 1, 604800, 60480, 26880, 16800, 14400, 6720, 3360, 2400, 1920, 1600, 840, 480, 400, 320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Each partition of n, ordered as in Abramowitz-Stegun (A-St order; for the reference see A134278), is mapped to a nonnegative integer a(n,k) =: M31hat(4;n,k) with the k-th partition of n in A-St order. The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...]. Fourth member (K=4) in the family M31hat(K) of partition number arrays. If M31hat(4;n,k) is summed over those k with fixed number of parts m one obtains the unsigned triangle S1hat(4):= A144886. LINKS Table of n, a(n) for n=1..58. W. Lang, First 10 rows of the array and more. W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3. FORMULA a(n,k) = product(|S1(4;j,1)|^e(n,k,j),j=1..n) with |S1(4;n,1)| = A049352(n,1) = A001715(n+2) = [1,4,20,120,840,6720,...] = (n+2)!/3!, 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. EXAMPLE [1];[4,1];[20,4,1];[120,20,16,4,1];[840,120,80,20,16,4,1];... a(4,3)= 16 = |S1(4;2,1)|^2. The relevant partition of 4 is (2^2). CROSSREFS A144887 (row sums). A144880 (M31hat(3) array). A144886 (S1hat(4)). Sequence in context: A249716 A333273 A128041 * A144886 A117380 A185420 Adjacent sequences: A144882 A144883 A144884 * A144886 A144887 A144888 KEYWORD nonn,easy,tabf AUTHOR Wolfdieter Lang Oct 09 2008, Oct 28 2008 STATUS approved

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Last modified November 29 10:33 EST 2023. Contains 367429 sequences. (Running on oeis4.)