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A134082 Triangle read by rows, (n-1) zeros followed by (2n, 1). 9
1, 2, 1, 0, 4, 1, 0, 0, 6, 1, 0, 0, 0, 8, 1, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 12, 1, 0, 0, 0, 0, 0, 0, 14, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums = (1, 3, 5, 7,...). A134082 * [1,2,3,...] = A084849: (1, 4, 11, 22, 37,...). Binomial transform of A134082 = A134083. A112295 replaces subdiagonal with (-1,-3,-5,...)

LINKS

Table of n, a(n) for n=0..35.

FORMULA

Triangle read by rows, (n-1) zeros followed by (2n, 1). As an infinite lower triangular matrix, (1,1,1,...) in the main diagonal and (2,4,6,8,...) in the subdiagonal.

From formalism in A132382, e.g.f. = I_o[2*(u*x)^(1/2)] (1+2x) where I_o is the zeroth modified Bessel function of the first kind, i.e. I_o[2*(u*x)^(1/2)] = sum(j=0,1,...) u^j/j! * x^j/j! . - Tom Copeland, Dec 07 2007

Row polynomial e.g.f.: exp(x*y)(1+2x). - Tom Copeland, Dec 03 2013

EXAMPLE

First few rows of the triangle are:

1;

2, 1;

0, 4, 1;

0, 0, 6, 1;

0, 0, 0, 8, 1;

0, 0, 0, 0, 10, 1;

...

CROSSREFS

Cf. A112295, A084849, A134083.

Sequence in context: A053117 A121448 A019094 * A185740 A139360 A326759

Adjacent sequences:  A134079 A134080 A134081 * A134083 A134084 A134085

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Oct 07 2007

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)