A086951 a(n) = n*3^n*(4*n - 1)/9.

0, 1, 14, 99, 540, 2565, 11178, 45927, 180792, 688905, 2558790, 9310059, 33303636, 117448461, 409209570, 1410975855, 4821232752, 16343405073, 55013709438, 184024732275, 612124372620, 2025821736981, 6673705343514, 21893519253879, 71548815908520, 233004367596825

Offset: 0

Author

Paul Barry, Jul 24 2003

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

Crossrefs

Binomial transform of A086950. Second binomial transform of decagonal numbers A001107. Binomial transform is A086952.

Programs

Mathematica

LinearRecurrence[{9,-27,27},{0,1,14},30] (* Harvey P. Dale, Apr 10 2023 *)

Formula

G.f.: x*(1 + 5*x)/(1 - 3*x)^3.

E.g.f.: exp(3*x)*x*(1 + 4*x). - Stefano Spezia, Oct 09 2022