A162583 G.f.: A(x) = exp( 6*Sum_{n>=1} A006519(n)*A038500(n) * x^n/n ).

1, 6, 24, 78, 222, 570, 1356, 3030, 6432, 13074, 25608, 48558, 89502, 160854, 282624, 486534, 822174, 1365978, 2234400, 3602742, 5732202, 9008034, 13993320, 21503730, 32711460, 49287750, 73598280, 108968334, 160041750, 233262786

Offset

0,2

Comments

A006519(n) = highest power of 2 dividing n and

A038500(n) = highest power of 3 dividing n.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + 6*x + 24*x^2 + 78*x^3 + 222*x^4 + 570*x^5 + 1356*x^6 + ...
log(A(x))/6 = x + 2*x^2/2 + 3*x^3/3 + 4*x^4/4 + x^5/5 + 6*x^6/6 + x^7/7 + 8*x^8/8 + 9*x^9/9 + ... + A006519(n)*A038500(n)*x^n/n + ...

Mathematica

nmax = 150; a[n_]:= SeriesCoefficient[Series[Exp[Sum[2^(IntegerExponent[k, 2] + 1)*3^(IntegerExponent[k, 3] + 1)*q^k/k, {k, 1, nmax}]], {q, 0, nmax}], n]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jul 04 2018 *)

Prog

(PARI) {a(n)=local(L=sum(m=1, n, 6*2^valuation(m, 2)*3^valuation(m, 3)*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

Crossrefs

Cf. A006519, A038500.

Sequence in context: A341364 A180437 A276179 * A259662 A058809 A140088

Adjacent sequences: A162580 A162581 A162582 * A162584 A162585 A162586

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2009

Status

approved