

A143690


a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, ...].


5



1, 7, 27, 70, 145, 261, 427, 652, 945, 1315, 1771, 2322, 2977, 3745, 4635, 5656, 6817, 8127, 9595, 11230, 13041, 15037, 17227, 19620, 22225, 25051, 28107, 31402, 34945, 38745, 42811, 47152, 51777, 56695, 61915, 67446, 73297, 79477, 85995, 92860
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OFFSET

0,2


COMMENTS

Binomial transform of [1, 6, 14, 9, 0, 0, 0,...].


LINKS



FORMULA

G.f.: (1 +3*x +5*x^2)/(1x)^4.
a(n) = (n+1)*(3*n^2 +2*n +2)/2.
E.g.f.: (1/2)*(2 +12*x +14*x^2 +3*x^3)*exp(x). (End)


EXAMPLE

a(3) = 70 = (1, 3, 3, 1) dot (1, 6, 14, 9) = (1 + 18 + 42 + 9). a(3) = 70 = sum of row 3 terms of triangle A033292: (13 + 16 + 19, + 22).


MATHEMATICA

Table[(n+1)*(3*n^2+2*n+2)/2, {n, 0, 50}] (* G. C. Greubel, May 30 2021 *)


PROG

(Sage) [(n+1)*(3*n^2+2*n+2)/2 for n in (0..50)] # G. C. Greubel, May 30 2021


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



