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Search: id:A116382
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| A116382 |
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Riordan array (1/sqrt(1-4x^2),(1-2x^2*c(x^2))(x^2*c(x^2))/(x(1-x-x^2*c(x^2))) where c(x) is the g.f. of A000108. |
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+0
13
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| 1, 0, 1, 2, 1, 1, 0, 3, 2, 1, 6, 4, 5, 3, 1, 0, 10, 10, 8, 4, 1, 20, 15, 21, 19, 12, 5, 1, 0, 35, 42, 42, 32, 17, 6, 1, 70, 56, 84, 92, 77, 50, 23, 7, 1, 0, 126, 168, 192, 180, 131, 74, 30, 8, 1, 252, 210, 330, 405, 400, 326, 210, 105, 38, 9, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are A116383. Diagonal sums are A116384. First column has e.g.f. Bessel_I(0,2x) (A000984 with interpolated zeros). Second column has e.g.f. Bessel_I(1,2x)+Bessel_I(2,2x) (A037952). Third column has e.g.f. Bessel_I(2,2x)+2*Bessel_I(3,2x)+Bessel_I(4,2x) (A116385). A binomial-Bessel triangle: column k has e.g.f. sum{j=0..k, C(k,j)*Bessel_I(k+j,2x)}.
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FORMULA
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Riordan array (1/sqrt(1-4x^2), sqrt(1-4x^2)(1-sqrt(1-4x^2))/(x-2x^2+x*sqrt(1-4x^2))); Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)*C(n,j)*sum{i=0..j, C(j,i-k)C(i,j-i)}}.
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EXAMPLE
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Triangle begins
1,
0, 1,
2, 1, 1,
0, 3, 2, 1,
6, 4, 5, 3, 1,
0, 10, 10, 8, 4, 1,
20, 15, 21, 19, 12, 5, 1,
0, 35, 42, 42, 32, 17, 6, 1,
70, 56, 84, 92, 77, 50, 23, 7, 1,
0, 126, 168, 192, 180, 131, 74, 30, 8, 1,
252, 210, 330, 405, 400, 326, 210, 105, 38, 9, 1
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CROSSREFS
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Sequence in context: A087117 A029340 A126258 this_sequence A050606 A023416 A080791
Adjacent sequences: A116379 A116380 A116381 this_sequence A116383 A116384 A116385
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 12 2006
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