A047674 Row 5 of square array defined in A047671.

1, 16, 91, 346, 1021, 2524, 5479, 10774, 19609, 33544, 54547, 85042, 127957, 186772, 265567, 369070, 502705, 672640, 885835, 1150090, 1474093, 1867468, 2340823, 2905798, 3575113, 4362616, 5283331, 6353506, 7590661, 9013636, 10642639, 12499294, 14606689, 16989424

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

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

Crossrefs

Cf. A047671.

Programs

PARI

my(x='x+O('x^35)); Vec(x*(1+10*x+10*x^2+20*x^3+5*x^4+2*x^5)/(1-x)^6) \\ Elmo R. Oliveira, Aug 30 2025

Formula

a(n) = (1/5)*(2*n^5 - 5*n^4 + 20*n^3 - 25*n^2 + 23*n - 10).

From Elmo R. Oliveira, Aug 30 2025: (Start)

G.f.: x*(1 + 10*x + 10*x^2 + 20*x^3 + 5*x^4 + 2*x^5)/(x-1)^6.

E.g.f.: 2 + (-10 + 15*x + 30*x^2 + 40*x^3 + 15*x^4 + 2*x^5)*exp(x)/5.

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 > 6. (End)

Extensions

More terms from Elmo R. Oliveira, Aug 30 2025