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A060102 Bisection of triangle A060098: even-indexed members of column sequences of A060098 (not counting leading zeros). 6
1, 1, 1, 1, 4, 1, 1, 9, 8, 1, 1, 16, 30, 13, 1, 1, 25, 80, 71, 19, 1, 1, 36, 175, 259, 140, 26, 1, 1, 49, 336, 742, 660, 246, 34, 1, 1, 64, 588, 1806, 2370, 1442, 399, 43, 1, 1, 81, 960, 3906, 7062, 6292, 2828, 610, 53 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums give A052975. Column sequences without leading zeros give for m=0..5: A000012 (powers of 1), A000290 (squares), A002417(n+1), A060103-5.
Companion triangle (odd-indexed members) A060556.
LINKS
FORMULA
a(n, m) = A060098(2*n-m, m).
a(n, m) = Sum_{j=0..floor((m+1)/2)} binomial((n-m)-j+2*m, 2*m)*binomial(m+1, 2*j), n >= m >= 0, otherwise zero.
G.f. for column m: (x^m)*Pe(m+1, x)/(1-x)^(2*m+1), with Pe(n, x) = Sum_{j=0..floor(n/2)} binomial(n, 2*j)*x^j (even members of row n of Pascal triangle A007318).
EXAMPLE
{1}; {1,1}; {1,4,1}; {1,9,8,1}; ... Pe(3,x) = 1 + 3*x.
CROSSREFS
Sequence in context: A114188 A110511 A082950 * A308359 A199065 A152237
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Apr 06 2001
STATUS
approved

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Last modified June 21 06:38 EDT 2024. Contains 373540 sequences. (Running on oeis4.)