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 A265604 Triangle read by rows: The inverse Bell transform of the quartic factorial numbers (A007696). 7
 1, 0, 1, 0, 1, 1, 0, -2, 3, 1, 0, 10, -5, 6, 1, 0, -80, 30, -5, 10, 1, 0, 880, -290, 45, 5, 15, 1, 0, -12320, 3780, -560, 35, 35, 21, 1, 0, 209440, -61460, 8820, -735, 0, 98, 28, 1, 0, -4188800, 1192800, -167300, 14700, -735, 0, 210, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Peter Luschny, The Bell transform Richell O. Celeste, Roberto B. Corcino, Ken Joffaniel M. Gonzales. Two Approaches to Normal Order Coefficients. Journal of Integer Sequences, Vol. 20 (2017), Article 17.3.5. EXAMPLE [ 1] [ 0,      1] [ 0,      1,      1] [ 0,     -2,      3,      1] [ 0,     10,     -5,      6,      1] [ 0,    -80,     30,     -5,     10,      1] [ 0,    880,   -290,     45,      5,     15,      1] PROG (Sage) # uses[bell_transform from A264428] def inverse_bell_matrix(generator, dim):     G = [generator(k) for k in srange(dim)]     row = lambda n: bell_transform(n, G)     M = matrix(ZZ, [row(n)+[0]*(dim-n-1) for n in srange(dim)]).inverse()     return matrix(ZZ, dim, lambda n, k: (-1)^(n-k)*M[n, k]) multifact_4_1 = lambda n: prod(4*k + 1 for k in (0..n-1)) print(inverse_bell_matrix(multifact_4_1, 8)) CROSSREFS Cf. A007696, A264428, A264429. Inverse Bell transforms of other multifactorials are: A048993, A049404, A049410, A075497, A075499, A075498, A119275, A122848, A265605. Sequence in context: A121434 A296455 A137329 * A171996 A175669 A288839 Adjacent sequences:  A265601 A265602 A265603 * A265605 A265606 A265607 KEYWORD sign,tabl AUTHOR Peter Luschny, Dec 30 2015 STATUS approved

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Last modified May 16 22:03 EDT 2021. Contains 343955 sequences. (Running on oeis4.)