A047661 Row 5 of square array defined in A047662.

5, 30, 115, 340, 841, 1826, 3591, 6536, 11181, 18182, 28347, 42652, 62257, 88522, 123023, 167568, 224213, 295278, 383363, 491364, 622489, 780274, 968599, 1191704, 1454205, 1761110, 2117835, 2530220, 3004545, 3547546, 4166431, 4868896, 5663141, 6557886, 7562387

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. A047662.

Programs

Mathematica

Table[(n/15)(2n^4+5n^3+20n^2+25n+23),{n,30}] (* Harvey P. Dale, Nov 25 2022 *)

PARI

my(x='x+O('x^35)); Vec(x*(5+10*x^2+x^4)/(1-x)^6) \\ Elmo R. Oliveira, Sep 02 2025

Formula

a(n) = (n/15)*(2*n^4 + 5*n^3 + 20*n^2 + 25*n + 23). [Corrected by Sean A. Irvine, May 13 2021]

From Elmo R. Oliveira, Sep 02 2025: (Start)

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

E.g.f.: x*(5 + 5*x + x^2)*(15 + 15*x + 2*x^2)*exp(x)/15.

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, Sep 02 2025