A377893 E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * exp(x * A(x)^3).

1, 2, 27, 742, 31337, 1796376, 130408603, 11472417104, 1186462228785, 141083381264896, 18966727953873371, 2844742575536036352, 470958524169176911513, 85307709328403287961600, 16782586179544965856158363, 3563492814539574559964993536, 812273035493592514001487147233

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = n! * Sum_{k=0..n} (3*n+1)^(k-1) * binomial(3*n+1,n-k)/k!.

a(n) ~ sqrt(sqrt(37)+7) * (sqrt(37)+1)^(3*n+1) * exp((3*(sqrt(37)-7)*n + sqrt(37)-5)/6) * n^(n-1) / (37^(1/4) * 2^(2*n + 3/2) * 3^(2*n+2) * (sqrt(37)-5)^n). - Vaclav Kotesovec, Jan 31 2026

Mathematica

Table[n! * Sum[(3*n+1)^(k-1) * Binomial[3*n+1, n-k]/k!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 31 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n, (3*n+1)^(k-1)*binomial(3*n+1, n-k)/k!);

Crossrefs

Cf. A088690, A377892.

Sequence in context: A138458 A090248 A300591 * A251693 A182934 A396804

Adjacent sequences: A377890 A377891 A377892 * A377894 A377895 A377896

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2024

Status

approved