A134083 - OEIS

%I #12 Mar 25 2022 19:37:05

%S 1,3,1,5,6,1,7,15,9,1,9,28,30,12,1,11,45,70,50,15,1,13,66,135,140,75,

%T 18,1,15,91,231,315,245,105,21,1,17,120,364,616,630,392,140,24,1,19,

%U 153,540,1092,1386,1134,588,180,27,1

%N A007318 * A134082.

%C Row sums = A001787: (1, 4, 12, 32, 80, 192, ...).

%C A134083 * [1,2,3,...] = A084850: (1, 5, 20, 68, 208, 592, ...).

%F Binomial transform of A134082

%F From formalism in A132382, e.g.f. = I_o[2*(u*x)^(1/2)] exp(x)(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} u^j/j! * x^j/j!. - _Tom Copeland_, Dec 07 2007

%F Row polynomial e.g.f.: exp(x*y) * exp(x) * (1+2x). - _Tom Copeland_, Dec 03 2013

%e First few rows of the triangle:

%e    1;

%e    3,  1;

%e    5,  6,   1;

%e    7, 15,   9,   1;

%e    9, 28,  30,  12,   1;

%e   11, 45,  70,  50,  15,   1;

%e   13, 66, 135, 140,  75,  18,  1;

%e   15, 91, 231, 315, 245, 105, 21, 1;

%e   ...

%Y Cf. A134082, A001787, A084850.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Oct 07 2007