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A064985 Number of partitions of n into factorial parts ( 0! allowed ). 4
1, 2, 4, 6, 9, 12, 17, 22, 29, 36, 45, 54, 66, 78, 93, 108, 126, 144, 166, 188, 214, 240, 270, 300, 336, 372, 414, 456, 504, 552, 608, 664, 728, 792, 864, 936, 1018, 1100, 1192, 1284, 1386, 1488, 1602, 1716, 1842, 1968, 2106, 2244, 2397, 2550, 2718, 2886 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: 1/(Product_{i>=1} (1-x^(i!)))/(1-x).

G.f.: 1/(1-x) + Sum_{n>0} x^(n!) / Product_{k=0..n} (1 - x^(k!)). - Seiichi Manyama, Oct 12 2019

EXAMPLE

a(3) = 6 because we can write 3 = 2!+1! = 2!+0! = 1!+1!+1! = 0!+0!+0! = 1!+1!+0! = 1!+0!+0!.

G.f.: 1/(1-x) + x/(1-x)^2 + x^2/((1-x)^2*(1-x^2)) + x^6/((1-x)^2*(1-x^2)*(1-x^6)) + ... . - Seiichi Manyama, Oct 12 2019

MATHEMATICA

nn=51; CoefficientList[Series[Product[1/(1-x^(i!)), {i, 0, 10}], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 29 2013 *)

PROG

(PARI) N=66; x='x+O('x^N); m=1; while(N>=m!, m++); Vec(1/prod(k=0, m-1, 1-x^k!)) \\ Seiichi Manyama, Oct 13 2019

(PARI) N=66; x='x+O('x^N); m=1; while(N>=m!, m++); Vec(1/(1-x)+sum(i=1, m-1, x^i!/prod(j=0, i, 1-x^j!))) \\ Seiichi Manyama, Oct 13 2019

CROSSREFS

Cf. A064986.

Sequence in context: A194450 A080556 A229093 * A090631 A001365 A102379

Adjacent sequences:  A064982 A064983 A064984 * A064986 A064987 A064988

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Oct 30 2001

EXTENSIONS

More terms from Vladeta Jovovic and Don Reble, Nov 02 2001

STATUS

approved

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Last modified February 28 06:55 EST 2020. Contains 332321 sequences. (Running on oeis4.)