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A308272 G.f. A(x) satisfies: A(x) = (1 + x) * A(x^2)*A(x^3)*A(x^5)* ... *A(x^prime(k))* ... 2
1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 13, 16, 22, 27, 33, 44, 53, 65, 84, 101, 124, 156, 187, 226, 280, 336, 403, 492, 587, 700, 850, 1008, 1195, 1435, 1693, 2004, 2390, 2808, 3303, 3910, 4584, 5372, 6328, 7387, 8619, 10106, 11757, 13675, 15961, 18508, 21464, 24948, 28845, 33345 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Weigh transform of A008480.

LINKS

Table of n, a(n) for n=0..53.

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^A008480(k).

MAPLE

g:= proc(n) option remember; (l-> add(i, i=l)!/

mul(i!, i=l))(map(i-> i[2], ifactors(n)[2]))

end:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(binomial(g(i), j)*b(n-i*j, i-1), j=0..n/i)))

end:

a:= n-> b(n$2):

seq(a(n), n=0..60); # Alois P. Heinz, May 17 2019

MATHEMATICA

terms = 53; A[_] = 1; Do[A[x_] = (1 + x) Product[A[x^Prime[k]], {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

CROSSREFS

Cf. A000040, A008480, A129373, A308271.

Sequence in context: A096981 A281966 A276431 * A035541 A187502 A236970

Adjacent sequences: A308269 A308270 A308271 * A308273 A308274 A308275

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 17 2019

STATUS

approved

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Last modified February 3 02:45 EST 2023. Contains 360024 sequences. (Running on oeis4.)