The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 19:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)