A145514
Number of partitions of n^n into powers of n, also diagonal of A145515 and A196879.
Original entry on oeis.org
1, 1, 4, 23, 1086, 642457, 6188114528, 1226373476385199, 6071277235712979102634, 884267692532264259002637317099, 4362395890943439751990308572939648140812, 824887275128335259519795007492785652798382136996397, 6674388542470138268339773975217339343278226845550864912413630534
Offset: 0
a(2) = 4, because there are 4 partitions of 2^2=4 into powers of 2: [1,1,1,1], [1,1,2], [2,2], [4].
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g:= proc(b,n,k) option remember; local t; if b<0 then 0 elif b=0 or n=0 or k<=1 then 1 elif b>=n then add(g(b-t, n, k) *binomial(n+1, t) *(-1)^(t+1), t=1..n+1); else g(b-1, n, k) +g(b*k, n-1, k) fi end: a:= n-> g(1,n,n): seq(a(n), n=0..13);
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g[b_, n_, k_] := g[b, n, k] = Which[b<0, 0, b == 0 || n == 0 || k <= 1, 1, b >= n, Sum[g[b-t, n, k] *Binomial[n+1, t]*(-1)^(t+1), {t, 1, n+1}], True, g[b-1, n, k] + g[b*k, n-1, k]]; a[n_] := g[1, n, n]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Feb 05 2017, translated from Maple *)
A196880
Number of partitions of n^2 into powers of 2.
Original entry on oeis.org
1, 1, 4, 10, 36, 94, 284, 692, 1828, 4124, 9828, 20798, 45564, 91018, 186788, 355906, 692004, 1264678, 2347716, 4138358, 7389572, 12625938, 21804900, 36243644, 60777212, 98547380, 160987868, 255297602, 407492292, 633469718, 990388828, 1512185428, 2320518948
Offset: 0
a(3) = 10, because there are 10 partitions of 3^2=9 into powers of 2: [1,8], [1,4,4], [1,2,2,4], [1,1,1,2,4], [1,1,1,1,1,4], [1,2,2,2,2], [1,1,1,2,2,2], [1,1,1,1,1,2,2], [1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1].
A196881
Number of partitions of n^3 into powers of 3.
Original entry on oeis.org
1, 1, 3, 23, 132, 729, 3987, 18687, 82350, 342383, 1295579, 4634280, 15873501, 51143461, 156932559, 463212189, 1309275981, 3576241449, 9484669665, 24306269493, 60475548510, 146630200929, 345755185335, 796397380425, 1797676089003, 3970398558042, 8602390112508
Offset: 0
A196882
Number of partitions of n^4 into powers of 4.
Original entry on oeis.org
1, 1, 6, 72, 1086, 15076, 182832, 1957192, 18583582, 154252476, 1166493640, 8049232896, 50660059120, 292884155232, 1582952988656, 8045405614080, 38559135542174, 174391413419872, 746859203235976, 3047000304533760, 11915800843394536, 44815994695641600
Offset: 0
a(2) = 6, because there are 6 partitions of 2^4=16 into powers of 4: [16], [4,4,4,4], [1,1,1,1,4,4,4], [1,1,1,1,1,1,1,1,4,4], [1,1,1,1,1,1,1,1,1,1,1,1,4], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].
A196883
Number of partitions of n^5 into powers of 5.
Original entry on oeis.org
1, 1, 9, 335, 15265, 642457, 21719504, 619319180, 14357878818, 288862888125, 4963576426547, 73352623884216, 969821344896765, 11543613849547500, 123338010592648600, 1190399192738655590, 10575211376139294058, 87409151426766072750, 674329967169731919750
Offset: 0
A196884
Number of partitions of n^6 into powers of 6.
Original entry on oeis.org
1, 1, 16, 2220, 374160, 53511471, 6188114528, 527457882126, 36521876237448, 1952615455825446, 86220169777616208, 3212254985375294550, 99345949328271872420, 2632974948301168473984, 61767819644161815082080, 1284454579537478675292282, 23584751451820642893522984
Offset: 0
A196885
Number of partitions of n^7 into powers of 7.
Original entry on oeis.org
1, 1, 36, 19166, 14615986, 8939918814, 3837284133564, 1226373476385199, 270102925553717303, 46188578538444709937, 5945914039134501155164, 595502415534028698326141, 49457500873761026837492373, 3353360710521929211582306983, 186523687141803451969677785640
Offset: 0
A196886
Number of partitions of n^8 into powers of 8.
Original entry on oeis.org
1, 1, 85, 217862, 880915707, 2723350958080, 5498735029150412, 6897556038713219072, 6071277235712979102634, 3511244471110991227215296, 1503179627327417142865920896, 477381405632773485831171726016, 111948028342925752822983662888144
Offset: 0
A196887
Number of partitions of n^9 into powers of 9.
Original entry on oeis.org
1, 1, 210, 3428059, 87935111811, 1541533772278182, 16177644099354374847, 101539033269801820825743, 365618223095981778848684187, 884267692532264259002637317099, 1357042381209389119735863425487474, 1470981941328093110877043096244300403
Offset: 0
A196888
Number of partitions of n^10 into powers of 10.
Original entry on oeis.org
1, 1, 586, 71688050, 13580513909670, 1659137949188540410, 104146398517005199125840, 3421092256089716422594644400, 64402239847567589358641684368970, 657656444358222872135019335879897500, 4362395890943439751990308572939648140812
Offset: 0
Showing 1-10 of 19 results.