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 A265606 Triangle read by rows: The Bell transform of the quartic factorial numbers (A007696). 4
 1, 0, 1, 0, 1, 1, 0, 5, 3, 1, 0, 45, 23, 6, 1, 0, 585, 275, 65, 10, 1, 0, 9945, 4435, 990, 145, 15, 1, 0, 208845, 89775, 19285, 2730, 280, 21, 1, 0, 5221125, 2183895, 456190, 62965, 6370, 490, 28, 1, 0, 151412625, 62002395, 12676265, 1715490, 171255, 13230, 798, 36, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS 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. Peter Luschny, The Bell transform EXAMPLE [1], [0, 1], [0, 1, 1], [0, 5, 3, 1], [0, 45, 23, 6, 1], [0, 585, 275, 65, 10, 1], [0, 9945, 4435, 990, 145, 15, 1], [0, 208845, 89775, 19285, 2730, 280, 21, 1], MATHEMATICA (* The function BellMatrix is defined in A264428. *) rows = 10; M = BellMatrix[Pochhammer[1/4, #] 4^# &, rows]; Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 23 2019 *) PROG (Sage) # uses[bell_transform from A264428] def A265606_row(n):     multifact_4_1 = lambda n: prod(4*k + 1 for k in (0..n-1))     mfact = [multifact_4_1(k) for k in (0..n)]     return bell_transform(n, mfact) [A265606_row(n) for n in (0..7)] CROSSREFS Cf. A007696, A264428, A264429. Bell transforms of other multifactorials are: A000369, A004747, A039683, A051141, A051142, A119274, A132062, A132393, A203412. Sequence in context: A126853 A286127 A201654 * A132199 A111142 A179626 Adjacent sequences:  A265603 A265604 A265605 * A265607 A265608 A265609 KEYWORD nonn,tabl AUTHOR Peter Luschny, Dec 30 2015 STATUS approved

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Last modified May 17 16:03 EDT 2021. Contains 343980 sequences. (Running on oeis4.)