A210779 Number of partitions of 2^n into powers of 2 less than or equal to 1024.

1, 2, 4, 10, 36, 202, 1828, 27338, 692004, 30251722, 2320518948, 316359580361, 77160820913241, 31769732129318865, 19210889607930498081, 14781930262928342616641, 13037860166110209522457729, 12369535268518332988593592577, 12186672180675798897571822711297

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..110

Index entries for linear recurrences with constant coefficients, signature (2047, -1396054, 407647768, -55440096448, 3634008902656, -116288284884992, 1816661080408064, -13678389311307776, 47968050187599872, -72022409665839104, 36028797018963968).

Formula

G.f.: (-95460882767931143880704*x^20 +143817459476148640546816*x^19 -47353367247905900986368*x^18 -1833431416452222550016*x^17 +851800662334219223040*x^16 -21573396097321885696*x^15 -5556995021730048*x^14 -2458328204903632*x^13 -3738333173327178*x^12 -5646507818862569*x^11 -16176670881134614*x^10 +26835366859855894*x^9 -10475796196345878*x^8 +1598080542315542*x^7 -109238000834070*x^6 +3524745413782*x^5 -54630364694*x^4 +404863838*x^3 -1391964*x^2 +2045*x-1) / Product_{j=0..10} (2^j*x-1).

a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..9} (1-x^(2^j)) for n>0.

Maple

gf:= (-1 +(2045 +(-1391964 +(404863838 +(-54630364694 +(3524745413782 +(-109238000834070 +(1598080542315542 +(-10475796196345878 +(26835366859855894 +(-16176670881134614 +(-5646507818862569 +(-3738333173327178 +(-2458328204903632 +(-5556995021730048 +(-21573396097321885696 +(851800662334219223040 +(-1833431416452222550016 +(-47353367247905900986368
+(143817459476148640546816 -95460882767931143880704*x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x)/ mul(2^j*x-1, j=0..10): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..20);

Crossrefs

Column k=10 of A152977.

Sequence in context: A210776 A210777 A210778 * A002577 A076132 A371999

Adjacent sequences: A210776 A210777 A210778 * A210780 A210781 A210782

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 26 2012

Status

approved