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A329757
Doubly octagonal pyramidal numbers.
4
0, 1, 765, 27435, 345415, 2469420, 12352956, 48294610, 157609530, 447989355, 1141711615, 2663460261, 5775482505, 11777133550, 22789550070, 42150245460, 74946834916, 128723876325, 214401953745, 347453633935, 549386792955, 849592039296, 1287617552320, 1915941609990, 2803320397950, 4038796372975
OFFSET
0,3
FORMULA
G.f.: x*(1 + 755*x + 19830*x^2 + 105370*x^3 + 158255*x^4 + 70629*x^5 + 7930*x^6 + 110*x^7)/(1 - x)^10.
a(n) = A002414(A002414(n)).
a(n) = Sum_{k=0..A002414(n)} A000567(k).
a(n) = n *(2*n-1) *(n+1) *(2*n^3+n^2-n+2) *(2*n^3+n^2-n-1) /8 . - R. J. Mathar, Nov 28 2019
MATHEMATICA
A002414[n_] := n (n + 1) (2 n - 1)/2; a[n_] := A002414[A002414[n]]; Table[a[n], {n, 0, 25}]
Table[Sum[k (3 k - 2), {k, 0, n (n + 1) (2 n - 1)/2}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[x (1 + 755 x + 19830 x^2 + 105370 x^3 + 158255 x^4 + 70629 x^5 + 7930 x^6 + 110 x^7)/(1 - x)^10, {x, 0, nmax}], x]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 765, 27435, 345415, 2469420, 12352956, 48294610, 157609530, 447989355}, 26]
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Nov 20 2019
STATUS
approved