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A116414
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Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))).
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2
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1, 4, 1, 13, 8, 1, 40, 42, 12, 1, 121, 184, 87, 16, 1, 364, 731, 496, 148, 20, 1, 1093, 2736, 2454, 1040, 225, 24, 1, 3280, 9844, 11064, 6170, 1880, 318, 28, 1, 9841, 34448, 46738, 32624, 13015, 3080, 427, 32, 1, 29524, 118101, 188208, 158724, 79044, 24381, 4704
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums are A116415. Diagonal sums are A007070. First column is A003462(n+1). Product of A007318 and A116412.
Subtriangle of triangle given by (0, 4, -3/4, 3/4, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - DELEHAM Philippe, Jan 18 2012
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FORMULA
| Riordan array (1/(1-4x+3x^2),x/(1-4x+3x^2)); Number triangle T(n,k)=sum{j=0..n, C(n-j,k)C(k+j,j)3^j}.
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EXAMPLE
| Triangle begins
1,
4, 1,
13, 8, 1,
40, 42, 12, 1,
121, 184, 87, 16, 1,
364, 731, 496, 148, 20, 1
Triangle T(n,k), 0<=k<=n, given by (0, 4, -3/4, 3/4, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, ...) begins :
1
0, 1
0, 4, 1
0, 13, 8, 1
0, 40, 42, 12, 1
0, 121, 184, 87, 16, 1
0, 364, 731, 496, 148, 20, 1
... - DELEHAM Philippe, Jan 18 2012
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CROSSREFS
| Cf. A003462, A116412
Sequence in context: A055252 A193956 A193843 * A144698 A115154 A051928
Adjacent sequences: A116411 A116412 A116413 * A116415 A116416 A116417
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 13 2006
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