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A304725
a(n) = n^4 + 8*n^3 + 20*n^2 + 16*n + 2.
0
2, 47, 194, 527, 1154, 2207, 3842, 6239, 9602, 14159, 20162, 27887, 37634, 49727, 64514, 82367, 103682, 128879, 158402, 192719, 232322, 277727, 329474, 388127, 454274, 528527, 611522, 703919, 806402, 919679, 1044482, 1181567, 1331714, 1495727, 1674434, 1868687
OFFSET
0,1
LINKS
Rigoberto Florez, Robinson A. Higuita and Antara Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.5 (see formula for B_4(x) on page 4).
FORMULA
G.f.: (2 + 37*x - 21*x^2 + 7*x^3 - x^4)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = A008865(n+2)^2 - 2. Therefore, a(n) is a member of A008865.
MATHEMATICA
Table[n^4 + 8 n^3 + 20 n^2 + 16 n + 2, {n, 0, 40}]
PROG
(Magma) [n^4+8*n^3+20*n^2+16*n+2: n in [0..40]];
CROSSREFS
Cf. A008865.
Fourth column of the array in A298675 (without -1).
Fifth column of the array in A299741.
Sequence in context: A264776 A153213 A355009 * A128822 A226420 A160922
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 30 2018
STATUS
approved