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A304659
a(n) = n*(n + 1)*(16*n - 1)/6.
2
0, 5, 31, 94, 210, 395, 665, 1036, 1524, 2145, 2915, 3850, 4966, 6279, 7805, 9560, 11560, 13821, 16359, 19190, 22330, 25795, 29601, 33764, 38300, 43225, 48555, 54306, 60494, 67135, 74245, 81840, 89936, 98549, 107695, 117390, 127650, 138491, 149929, 161980, 174660, 187985
OFFSET
0,2
FORMULA
O.g.f.: x*(5 + 11*x)/(1 - x)^4.
E.g.f.: x*(30 + 63*x + 16*x^2)*exp(x)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) + a(-n) = A033429(n).
a(n) = n*A007742(n) - Sum_{k = 0..n-1} A007742(k) for n > 0.
Also, this sequence is related to A076455 by the same type of recurrence:
A076455(n) = n*a(n) - Sum_{k = 0..n-1} a(k) for n > 0.
MATHEMATICA
Table[n (n + 1) (16 n - 1)/6, {n, 0, 50}]
PROG
(Magma) [n*(n+1)*(16*n-1)/6: n in [0..41]]; // Vincenzo Librandi, May 23 2018
(PARI) concat(0, Vec(x*(5 + 11*x) / (1 - x)^4 + O(x^40))) \\ Colin Barker, May 25 2018
CROSSREFS
Cf. A007742, A076455, A139273 (first differences).
First lower diagonal of the rectangular array in A213835.
Sequence in context: A213068 A138657 A106909 * A115519 A211923 A362304
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, May 22 2018
STATUS
approved