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 A213947 Triangle read by rows: columns are finite differences of the INVERT transform of (1, 2, 3,...) terms 2
 1, 1, 2, 1, 4, 3, 1, 10, 6, 4, 1, 20, 21, 8, 5, 1, 42, 57, 28, 10, 6, 1, 84, 150, 88, 35, 12, 7, 1, 170, 390, 252, 110, 42, 14, 8, 1, 340, 990, 712, 335, 132, 49, 16, 9, 1, 682, 2475, 1992, 975, 402, 154, 56, 18, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Create an array in which the n-th row is the output of the INVERT transform on the first n natural numbers followed by zeros: 1,...1,...1,...1,...1,...1,...1,... 1,...3,...5,..11,..21,..43,..85,... (A001045) 1,...3,...8,..17,..42,.100,.235,... (A101822) 1,...3,...8,..21,..50,.128,.323,... For example, row 3 is the INVERT transform of (1, 2, 3, 0, 0, 0,...). Then, take finite differences of column terms starting from the top; which become the rows of the triangle. LINKS EXAMPLE First few rows of the triangle are: 1; 1, 2; 1, 4, 3; 1, 10, 6, 4; 1, 20, 21, 8, 5; 1, 42, 57, 28, 10, 6; 1, 84, 150, 88, 35, 12, 7; 1, 170, 390, 252, 110, 42, 14, 8; 1, 340, 990, 712, 335, 132, 49, 16, 9; 1, 682, 2475, 1992, 975, 402, 154, 56 18, 10; 1, 1364, 6138, 5464, 2805, 1200, 469, 176, 63, 20, 11; ... MAPLE read("transforms") ; A213947i := proc(n, k)         L := [seq(i, i=1..n), seq(0, i=0..k)] ;         INVERT(L) ;         op(k, %) ; end proc: A213947 := proc(n, k)         if k = 1 then                 1;         else         A213947i(k, n)-A213947i(k-1, n) ;         end if; end proc: # R. J. Mathar, Jun 30 2012 CROSSREFS Cf. A001906 (row sums), A026644 (2nd column) Sequence in context: A319075 A264871 A067410 * A188403 A248929 A109977 Adjacent sequences:  A213944 A213945 A213946 * A213948 A213949 A213950 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jun 25 2012 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)