A323220 a(n) = n*(n + 5)*(n + 7)*(n + 10)/24 + 1.

1, 23, 64, 131, 232, 376, 573, 834, 1171, 1597, 2126, 2773, 3554, 4486, 5587, 6876, 8373, 10099, 12076, 14327, 16876, 19748, 22969, 26566, 30567, 35001, 39898, 45289, 51206, 57682, 64751, 72448, 80809, 89871, 99672, 110251, 121648, 133904, 147061, 161162, 176251

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = [x^n] (8*x^4 - 31*x^3 + 41*x^2 - 18*x - 1)/(x - 1)^5.

a(n) = n! [x^n] exp(x)*(x^4 + 28*x^3 + 228*x^2 + 528*x + 24)/24.

a(n) = (1/3)*((2*n + 17)*a(n-3) - (3*n + 25)*a(n-2) + (n + 15)*a(n-1)) for n >= 3.

a(n) = A323224(n, 5).

Maple

a := n -> (n^4 + 22*n^3 + 155*n^2 + 350*n + 24)/24:
seq(a(n), n=0..40);

Mathematica

A323220[n_] := n*(n + 5)*(n + 7)*(n + 10)/24 + 1;
Array[A323220, 50, 0] (* Paolo Xausa, Jul 09 2026 *)

Crossrefs

Cf. A323224 (column 5), A323233 (row 5), A323221 (first diff.), A034856 (second diff.).

Sequence in context: A089823 A304896 A316578 * A001346 A051875 A125872

Adjacent sequences: A323217 A323218 A323219 * A323221 A323222 A323223

Keyword

nonn,easy,changed

Author

Peter Luschny, Jan 25 2019

Status

approved