A216967 G.f.: Sum_{n>=0} (3*n)!/2^n * x^n / Product_{k=1..n} (1 + k^3*x).

1, 3, 177, 43743, 28317777, 37918359903, 91064083658577, 356470099797125343, 2123580647871774583377, 18282562085069810089566303, 218479480936045179472923760977, 3508620018746019243855156135806943, 73737548542861221762649623289597264977

Offset

0,2

Comments

Compare to the o.g.f. for Euler numbers (A000364):

Sum_{n>=0} (2*n)!/2^n * x^n / Product_{k=1..n} (1 + k^2*x).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..100

L. Naughton, G. Pfeiffer, Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group, J. Int. Seq. 16 (2013) #13.5.8

Formula

a(n) == 0 (mod 3) for n>0;

a(n) == 3 (mod 6) for n>0;

a(2*n-1) == 3 (mod 5), a(2*n) == 2 (mod 5), for n>0;

a(2*n-1) == 3 (mod 9), a(2*n) == 6 (mod 9), for n>0;

a(2*n-1) == 3 (mod 10), a(2*n) == 7 (mod 10), for n>0.

a(n) ~ c * 2^(3/2) * Pi^(3/2) * d^n * n^(3*n+1/2) / exp(3*n), where d = 13.2458829063958687527098..., c = 0.281041890716214414121... . - Vaclav Kotesovec, Dec 05 2015

Example

G.f.: A(x) = 1 + 3*x + 177*x^2 + 43743*x^3 + 28317777*x^4 +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, (3*m)!/2^m*x^m/prod(k=1, m, 1+k^3*x+x*O(x^n))), n)}
for(n=0, 21, print1(a(n), ", "))

Crossrefs

Sequence in context: A113270 A091324 A198446 * A217443 A270245 A093434

Adjacent sequences: A216964 A216965 A216966 * A216968 A216969 A216970

Keyword

nonn

Author

Paul D. Hanna, Sep 20 2012

Status

approved