A365373 a(n) = n*(3*n^4 + 15*n^3 + 25*n^2 - 15*n - 28)/60.

0, 0, 7, 40, 136, 356, 791, 1568, 2856, 4872, 7887, 12232, 18304, 26572, 37583, 51968, 70448, 93840, 123063, 159144, 203224, 256564, 320551, 396704, 486680, 592280, 715455, 858312, 1023120, 1212316, 1428511, 1674496, 1953248, 2267936, 2621927, 3018792, 3462312

Offset: 0

Author

Stefano Spezia, Sep 02 2023

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Antidiagonal sums of A365372.

Cf. A068601 (2nd differences).

Programs

Mathematica

a[n_]:= n*(3*n^4 + 15*n^3 + 25*n^2 - 15*n - 28)/60; Array[a,37,0]

Python

def A365373(n): return n*(n*(n*(n*(3*n + 15) + 25) - 15) - 28)//60 # Chai Wah Wu, Sep 04 2023

Formula

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.

O.g.f.: x^2*(7 - 2*x + x^2)/(1 - x)^6.

E.g.f.: exp(x)*x^2*(210 + 190*x + 45*x^2 + 3*x^3)/60.