A210778 Number of partitions of 2^n into powers of 2 less than or equal to 512.

1, 2, 4, 10, 36, 202, 1828, 27338, 692004, 30251722, 2320518947, 314039061413, 69808185542089, 22148021690928529, 8756818568093328161, 3918553907116206319169, 1872922535299778812595329, 926165546297497921388714241, 465979162430464375966575440385

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..120

Index entries for linear recurrences with constant coefficients, signature (1023, -348502, 50781720, -3439615168, 111842970624, -1761082966016, 13312123207680, -46775146643456, 70300024700928, -35184372088832).

Formula

G.f.: (-537373113935986688*x^17 +691978531999055872*x^16 -160490503232552960*x^15 +5811316119175168*x^14 +75591601244160*x^13 -4465138103744*x^12 -3652534938428*x^11 -5517732454379*x^10 -15802918567958*x^9 +26190980411414*x^8 -10204692593686*x^7 +1550660009494*x^6 -105163418774*x^5 +3339435542*x^4 -50088798*x^3 +346460*x^2 -1021*x+1) / Product_{j=0..9} (2^j*x-1).

a(n) = [x^2^(n-1)] 1/(1-x) * 1/Product_{j=0..8} (1-x^(2^j)) for n>0.

Maple

gf:= (1+ (-1021 +(346460 +(-50088798 +(3339435542 +(-105163418774 +(1550660009494 +(-10204692593686 +(26190980411414 +(-15802918567958 +(-5517732454379 +(-3652534938428 +(-4465138103744 +(75591601244160 +(5811316119175168 +(-160490503232552960 +(691978531999055872 -537373113935986688*x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x) *x)/ mul(2^j*x-1, j=0..9): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..20);

Crossrefs

Column k=9 of A152977.

Sequence in context: A210775 A210776 A210777 * A210779 A002577 A076132

Adjacent sequences: A210775 A210776 A210777 * A210779 A210780 A210781

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 26 2012

Status

approved