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

1,1

Links

Table of n, a(n) for n=1..35.

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

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A047662.

Sequence in context: A062990 A018213 A359975 * A000649 A027173 A286973

Adjacent sequences: A047658 A047659 A047660 * A047662 A047663 A047664

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Elmo R. Oliveira, Sep 02 2025

Status

approved