A153583 - OEIS

%I #8 Jan 28 2019 08:09:30

%S 1,2,1,3,2,3,4,3,6,9,5,4,9,18,24,6,5,12,27,48,65,7,6,15,36,72,130,177,

%T 8,7,18,45,96,195,354,481,9,8,21,54,120,260,531,962,1308,10,9,24,63,

%U 144,325,708,1443,2616,3555,11,10,27,72,168,390,885,1924,3924,7110,9664

%N Convolution triangle by rows, A004736 * (A153582 * 0^(n-k)).

%C Row sums = A024581: (1, 3, 8, 22, 60, 163,...).

%C Right border = A153582.

%H Steve Butler, R. L. Graham & Nan Zang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Butler/butler8.html">Jumping Sequences</a>, Journal of Integer Sequences, Vol. 11, 2008, 08.4.5.

%F Convolution triangle by rows, A004736 * (A153582 * 0^(n-k)).

%e First few rows of the triangle =

%e   1;

%e   2, 1;

%e   3, 2, 3;

%e   4, 3, 6, 9;

%e   5, 4, 9, 18, 24;

%e   6, 5, 12, 27, 48, 65;

%e   7, 6, 15, 36, 72, 130, 177;

%e   8, 7, 18, 45, 96, 195, 354, 481;

%e   9, 8, 21, 54, 120, 260, 531, 962, 1308;

%e   10, 9, 24, 63, 144, 325, 708, 1443, 2616, 3555;

%e   ...

%e Row 3 = (4, 3, 6, 9) = termwise products of (4, 3, 2, 1) and (1, 1, 3, 9);

%e where A153582 = (1, 1, 3, 9, 24, 65,...).

%o (PARI) tabl(nn) = {my(va = vector(nn), vc = vector(nn)); va[1] = 1; for (n=1, nn, if (n > 1, va[n] = round(exp(1)*va[n-1])); vc[n] = va[n] - sum(k=1, n-1, vc[k]*(n-k+1)); print(vector(n, k, vc[k]*(n-k+1))););} \\ _Michel Marcus_, Jan 28 2019

%Y Cf. A024581, A153582, A004736

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Dec 28 2008

%E More terms from _Michel Marcus_, Jan 28 2019