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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

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

FORMULA

a(n, m)= A060098(2*n-m, m).

a(n, m)= sum(binomial((n-m)-j+2*m, 2*m)*binomial(m+1, 2*j), j=0..floor((m+1)/2)), n >= m >= 0, else zero.

G.f. for column m: (x^m)*Pe(m+1, x)/(1-x)^(2*m+1), with Pe(n, x)=sum(binomial (n, 2*j)*x^j, j=0..floor(n/2)) (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 * A199065 A152237 A176282

Adjacent sequences:  A060099 A060100 A060101 * A060103 A060104 A060105

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 06 2001

STATUS

approved

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Last modified March 26 05:43 EDT 2019. Contains 321481 sequences. (Running on oeis4.)