A376778 a(n) = (32*n^4 + 80*n^3 + 40*n^2 - 20*n + 3)*(2*n + 1)*n/15.

0, 27, 850, 7077, 33300, 113311, 312390, 742665, 1581544, 3093219, 5653242, 9776173, 16146300, 25651431, 39419758, 58859793, 85703376, 122051755, 170424738, 233812917, 315732964, 420285999, 552219030, 716989465, 920832696, 1170832755, 1474996042, 1842328125, 2282913612, 2807999095, 3430079166, 4162985505, 5021979040, 6023845179, 7186992114, 8531552197, 10079486388

Offset: 0

Author

N. J. A. Sloane, Nov 10 2024, following a suggestion from Fredrik Johansson (see A376777)

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A376777, A014105, A377858.

Programs

Python

def A376778(n): return n*(n*(n**2*(n*(n+3<<6)+160)-14)+3)//15 # Chai Wah Wu, Nov 11 2024

Formula

From Stefano Spezia, Nov 12 2024: (Start)

G.f.: x*(27 + 661*x + 1694*x^2 + 666*x^3 + 23*x^4 + x^5)/(1 - x)^7.

E.g.f.: exp(x)*x*(405 + 5970*x + 11520*x^2 + 6240*x^3 + 1152*x^4 + 64*x^5)/15. (End)