A213546 Principal diagonal of the convolution array A213505.

1, 25, 170, 674, 1979, 4795, 10164, 19524, 34773, 58333, 93214, 143078, 212303, 306047, 430312, 592008, 799017, 1060257, 1385746, 1786666, 2275427, 2865731, 3572636, 4412620, 5403645, 6565221, 7918470, 9486190, 11292919, 13364999, 15730640, 18419984, 21465169

Offset: 1

Author

Clark Kimberling, Jun 16 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A213505, A213500.

Programs

Mathematica

(See A213505.)
LinearRecurrence[{6,-15,20,-15,6,-1},{1,25,170,674,1979,4795},40] (* Harvey P. Dale, May 12 2025 *)

Formula

a(n) = (16*n^5 + 15*n^4 - n)/30.

a(n) = 6*a(n-1) - 10*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

G.f.: x*(1 + 19*x + 35*x^2 + 9*x^3)/(1 - x)^6.

E.g.f.: exp(x)*x*(30 + 345*x + 490*x^2 + 175*x^3 + 16*x^4)/30. - Stefano Spezia, Oct 28 2023