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
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).
Crossrefs
Column k=9 of A152977.
Programs
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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);
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.