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 A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3,...). 2
 1, 1, 2, 1, 2, 5, 1, 2, 2, 16, 1, 2, 2, 5, 45, 1, 2, 2, 2, 12, 125, 1, 2, 2, 2, 5, 24, 341, 1, 2, 2, 2, 2, 12, 48, 918, 1, 2, 2, 2, 2, 7, 18, 97, 2453, 1, 2, 2, 2, 2, 2, 16, 28, 195, 6515 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums = A001906, the even indexed Fibonacci numbers starting (1, 3, 8, 21,...). LINKS FORMULA Given S(x) = (1 + 2x + 3x^2 + ...), where (1, 2, 3,...) = the INVERTi transform of (1, 3, 8, 21, 55,...); k-th row of the array = INVERT transform of S(x^k). Take finite differences of array columns starting from the topmost "1"; becoming rows of the triangle. EXAMPLE First few rows of the array = 1, 3, 8, 21, 55, 144, 377, 987, 2584,... 1, 1, 3,..5, 10,..19,..36,..69,..131,... 1, 1, 1,..3,..5,...7,..12,..21,...34,... 1, 1, 1,..1,..3,...5,...7,...9,...16,... 1, 1, 1,..1,..1,...3,...5,...7,....9,... 1, 1, 1,..1,..1,...1,...3,...5,....7,... ... Taking finite differences from the bottom to top starting with the last "1" we obtain triangle A175011: 1; 1, 2; 1, 2, 5; 1, 2, 2, 16; 1, 2, 2, 5, 45; 1, 2, 2, 2, 12, 125; 1, 2, 2, 2, 5, 24, 341; 1, 2, 2, 2, 2, 12, 48, 918; 1, 2, 2, 2, 2, 7, 18, 97, 2453; 1, 2, 2, 2, 2, 2, 16, 28, 195, 6515; ... CROSSREFS Cf. A001906 Sequence in context: A245841 A011404 A002211 * A211700 A171840 A132309 Adjacent sequences:  A175008 A175009 A175010 * A175012 A175013 A175014 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Apr 03 2010 STATUS approved

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Last modified January 23 04:40 EST 2019. Contains 319370 sequences. (Running on oeis4.)