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 A325616 Triangle read by rows where T(n,k) is the number of length-k integer partitions of n into factorial numbers. 10
 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,61 LINKS FORMULA T(n,k) is the coefficient of x^n * y^k in the expansion of Product_{i > 0} 1/(1 - y * x^(i!)). EXAMPLE Triangle begins:   1   0 1   0 1 1   0 0 1 1   0 0 1 1 1   0 0 0 1 1 1   0 1 0 1 1 1 1   0 0 1 0 1 1 1 1   0 0 1 1 1 1 1 1 1   0 0 0 1 1 1 1 1 1 1   0 0 0 1 1 2 1 1 1 1 1   0 0 0 0 1 1 2 1 1 1 1 1   0 0 1 0 1 1 2 2 1 1 1 1 1   0 0 0 1 0 1 1 2 2 1 1 1 1 1   0 0 0 1 1 1 1 2 2 2 1 1 1 1 1   0 0 0 0 1 1 1 1 2 2 2 1 1 1 1 1   0 0 0 0 1 1 2 1 2 2 2 2 1 1 1 1 1   0 0 0 0 0 1 1 2 1 2 2 2 2 1 1 1 1 1   0 0 0 1 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1   0 0 0 0 1 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1   0 0 0 0 1 1 1 1 2 2 3 2 2 2 2 2 1 1 1 1 1 Row n = 12 counts the following partitions:   (66)   (6222)   (62211)   (222222) (621111)   (2222211) (6111111)   (22221111)   (222111111)   (2211111111)   (21111111111)   (111111111111) MATHEMATICA Table[SeriesCoefficient[Product[1/(1-y*x^(i!)), {i, 1, n}], {x, 0, n}, {y, 0, k}], {n, 0, 15}, {k, 0, n}] CROSSREFS Row sums are A064986. Cf. A008284. Factorial numbers: A000142, A007489, A076934, A108731, A115944, A227157, A284605, A322583, A325509, A325617. Reciprocal factorial sum: A325618, A325619, A325620, A325622. Sequence in context: A218245 A086075 A316865 * A056978 A321761 A037819 Adjacent sequences:  A325613 A325614 A325615 * A325617 A325618 A325619 KEYWORD nonn,tabl AUTHOR Gus Wiseman, May 12 2019 STATUS approved

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)