cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A306489 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of 1/(1 - Sum_{d|k} x^d).

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%I A306489 #7 Feb 21 2019 04:17:22
%S A306489 1,1,1,1,1,1,1,1,2,1,1,1,1,3,1,1,1,2,2,5,1,1,1,1,3,3,8,1,1,1,2,1,6,4,
%T A306489 13,1,1,1,1,4,1,10,6,21,1,1,1,2,1,7,2,18,9,34,1,1,1,1,3,1,13,3,31,13,
%U A306489 55,1,1,1,2,2,6,1,25,4,55,19,89,1,1,1,1,3,3,10,1,46,5,96,28,144,1
%N A306489 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of 1/(1 - Sum_{d|k} x^d).
%C A306489 A(n,k) is the number of compositions (ordered partitions) of n into divisors of k.
%F A306489 G.f. of column k: 1/(1 - Sum_{d|k} x^d).
%e A306489 Square array begins:
%e A306489   1,  1,  1,   1,  1,   1,  ...
%e A306489   1,  1,  1,   1,  1,   1,  ...
%e A306489   1,  2,  1,   2,  1,   2,  ...
%e A306489   1,  3,  2,   3,  1,   4,  ...
%e A306489   1,  5,  3,   6,  1,   7,  ...
%e A306489   1,  8,  4,  10,  2,  13,  ...
%t A306489 Table[Function[k, SeriesCoefficient[1/(1 - Sum[x^d, {d, Divisors[k]}]), {x, 0, n}]][i - n + 1], {i, 0, 12}, {n, 0, i}] // Flatten
%Y A306489 Columns k=1..7 give A000012, A000045 (for n > 0), A000930, A060945, A003520, A079958, A005709.
%Y A306489 Cf. A100346, A214575.
%K A306489 nonn,tabl
%O A306489 0,9
%A A306489 _Ilya Gutkovskiy_, Feb 19 2019