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 A099575 Number triangle T(n,k)=binomial(n+floor(k/2)+1,n+1), 0<=k<=n. 5
 1, 1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 6, 21, 1, 1, 7, 7, 28, 28, 1, 1, 8, 8, 36, 36, 120, 1, 1, 9, 9, 45, 45, 165, 165, 1, 1, 10, 10, 55, 55, 220, 220, 715, 1, 1, 11, 11, 66, 66, 286, 286, 1001, 1001, 1, 1, 12, 12, 78, 78, 364, 364, 1365, 1365, 4368, 1, 1, 13, 13, 91, 91, 455, 455 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are A099576. Diagonal sums are A099577. Main diagonal is A099578. Original name was: "Number triangle T(n,k)=if(k<=n,sum{j=0..floor(k/2),binomial(n+j,j)},0)." LINKS Robert Israel, Table of n, a(n) for n = 0..10010 (Rows 0..140, flattened) EXAMPLE Rows start:   {1},   {1,1},   {1,1,4},   {1,1,5,5},   {1,1,6,6,21},   ... MAPLE for n from 0 to 20 do seq(binomial(n+floor(k/2)+1, n+1), k=0..n) od; # Robert Israel, May 08 2018 CROSSREFS Cf. A099573, A099576, A099577, A099578. Sequence in context: A016522 A153843 A318795 * A173740 A028275 A173118 Adjacent sequences:  A099572 A099573 A099574 * A099576 A099577 A099578 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Oct 23 2004 EXTENSIONS Definition simplified by Robert Israel, May 08 2018 STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)