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

Author

Wolfdieter Lang, Apr 06 2001

Keywords

• nonn
• easy
• tabl

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.

Examples

			{1}; {1,1}; {1,4,1}; {1,9,8,1}; ... Pe(3,x) = 1 + 3*x.
		

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).