A060102 Bisection of triangle A060098: even-indexed members of column sequences of A060098 (not counting leading zeros).

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

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

Table of n, a(n) for n=0..53.

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

Adjacent sequences: A060099 A060100 A060101 * A060103 A060104 A060105

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Apr 06 2001

Status

approved