A213846 Antidiagonal sums of the convolution array A213844.

3, 23, 90, 250, 565, 1113, 1988, 3300, 5175, 7755, 11198, 15678, 21385, 28525, 37320, 48008, 60843, 76095, 94050, 115010, 139293, 167233, 199180, 235500, 276575, 322803, 374598, 432390, 496625, 567765

Offset: 1

Author

Clark Kimberling, Jul 05 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A213846.

Programs

Mathematica

(See A213846.)

Formula

a(n) = n*(1 + n)*(1 - 2*n + 4*n^2)/6.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: f(x)/g(x), where f(x) = x*(3 + 8*x + 5*x^2) and g(x) = (1-x)^5.