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 A178616 Triangle by columns, odd columns of Pascal's triangle A007318, else (1, 0, 0, 0,...) 4
 1, 0, 1, 0, 2, 1, 0, 3, 0, 1, 0, 4, 0, 4, 1, 0, 5, 0, 10, 0, 1, 0, 6, 0, 20, 0, 6, 1, 0, 7, 0, 35, 0, 21, 0, 1, 0, 8, 0, 56, 0, 56, 0, 8, 0, 1, 0, 9, 0, 84, 0, 126, 0, 36, 0, 1, 0, 10, 0, 120, 0, 252, 0, 120, 0, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = a variant of A052950, starting (1, 1, 3, 4, 9, 16, 33,...); whereas A052950 starts (2, 1, 3, 4, 9,...). Column 1 of the inverse of A178616 is a signed variant of A065619 prefaced with an 0; where A065619 = (1, 2, 3, 8, 25, 96, 427,...). LINKS FORMULA Triangle, odd columns of Pascal's triangle; (1, 0, 0, 0,...) as even columns k. Alternatively, (since A178616 + A162169 - Identity matrix) = Pascal's triangle, we can begin with Pascal's triangle, subtract A162169, then add the Identity matrix to obtain A178616. EXAMPLE First few rows of the triangle = 1, 0, 1; 0, 2, 1; 0, 3, 0, 1 0, 4, 0, 4, 1; 0, 5, 0, 10, 0, 1; 0, 6, 0, 20, 0, 6, 1; 0, 7, 0, 35, 0, 21, 0, 1; 0, 8, 0, 56, 0, 56, 0 8, 1; 0, 9, 0, 84, 0, 126, 0, 36, 0, 1; 0, 10, 0, 120, 0, 252, 0, 120, 0, 10, 1; 0, 11, 0, 165, 0, 462, 0, 330, 0, 55, 0, 1; ... CROSSREFS Cf. A162109, A065619, A052950, A095704. Sequence in context: A159813 A157409 A245960 * A165252 A127373 A200123 Adjacent sequences:  A178613 A178614 A178615 * A178617 A178618 A178619 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, May 30 2010 STATUS approved

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Last modified August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)