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

1,2

Links

Table of n, a(n) for n=1..34.

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

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)

Prog

(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

Crossrefs

Cf. A047671.

Sequence in context: A195591 A240292 A050406 * A153029 A170920 A027938

Adjacent sequences: A047671 A047672 A047673 * A047675 A047676 A047677

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Elmo R. Oliveira, Aug 30 2025

Status

approved