

A125577


a(0) = 1; for n >= 1, a(n) = n^2  a(n1).


3



1, 0, 4, 5, 11, 14, 22, 27, 37, 44, 56, 65, 79, 90, 106, 119, 137, 152, 172, 189, 211, 230, 254, 275, 301, 324, 352, 377, 407, 434, 466, 495, 529, 560, 596, 629, 667, 702, 742, 779, 821, 860, 904, 945, 991, 1034, 1082, 1127, 1177, 1224, 1276, 1325, 1379, 1430
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OFFSET

0,3


COMMENTS

A sequence given by a recurrence that is almost polynomial; it cannot be expressed as a polynomial, but is bounded by n^2.
If we let a(0) = 0, the triangular numbers result; a typo led to the new sequence.


LINKS



FORMULA

O.g.f.: (1+2*x4*x^2+x^3)/((1+x)^3*(1+x)). a(n) = n1+(1)^n+A000217(n+1).  R. J. Mathar, Dec 05 2007


EXAMPLE

a(0)=1, so a(1) = 1^2  1 = 0; a(2) = 2^2  0 = 4; a(3) = 9  4 = 5; etc.


MATHEMATICA

a[0] := 1 a[n_] := n^2  a[n  1]
CoefficientList[Series[(1 + 2 x  4 x^2 + x^3)/((1 + x)^3 (1 + x)), {x, 0, 50}], x] (* Vincenzo Librandi, May 19 2014 *)


PROG

(Python)
a = 1
for n in range(1, 77):
print(a, end=', ')
a = n*n  a
(Magma) [1] cat [n le 1 select n1 else n^2Self(n1): n in [1..50]]; // Vincenzo Librandi, May 19 2014


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

John C. George (John.George(AT)ENMU.edu), Jan 03 2007


EXTENSIONS



STATUS

approved



