A196879 -id:A196879 - cp's OEIS frontend

A196889 Number of partitions of 2^n into powers of n.

1, 1, 4, 3, 6, 9, 16, 36, 85, 210, 586, 1914, 6930, 28178, 125440, 603350, 3083410, 17362239, 112403052, 820563290, 6632950912, 58209665965, 544071039000, 5353538904357, 58523908575096, 730174875609318, 10274727352967428, 159586345364505768

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

			a(3) = 3 because there are 3 partitions of 2^3=8 into powers of 3: [1,1,3,3], [1,1,1,1,1,3], [1,1,1,1,1,1,1,1].

Alois P. Heinz, Table of n, a(n) for n = 0..150

Row n=2 of A196879.

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

A196890 Number of partitions of 3^n into powers of n.

Original entry on oeis.org

1, 1, 10, 23, 72, 335, 2220, 19166, 217862, 3428059, 71688050, 1884401480, 63363038340, 2929516409504, 178211319638172, 13290584617658383, 1240111930777216192, 158642776309162956097, 26642849845285577276244, 5432337767302682299726906

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

			a(2) = 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].

Alois P. Heinz, Table of n, a(n) for n = 0..100

Row n=3 of A196879.

a(n) = [x^(3^n)] 1/Product_{j>=0}(1-x^(n^j)) for n>1.

A196891 Number of partitions of 4^n into powers of n.

Original entry on oeis.org

1, 1, 36, 132, 1086, 15265, 374160, 14615986, 880915707, 87935111811, 13580513909670, 3070403347926710, 1135311726763434816, 641959330240781369240, 510702153600297288442786, 653871437018428663002896250, 1287709155623146652148156476562

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..100

Row n=4 of A196879.

a(n) = [x^(4^n)] 1/Product_{j>=0}(1-x^(n^j)) for n>1.

A196892 Number of partitions of 5^n into powers of n.

Original entry on oeis.org

1, 1, 94, 729, 15076, 642457, 53511471, 8939918814, 2723350958080, 1541533772278182, 1659137949188540410, 3004476086657587282943, 10324888948772382935056000, 62412485736933252992029397897, 625874099080778019949864563475382

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..50

Row n=5 of A196879.

a(n) = [x^(5^n)] 1/Product_{j>=0}(1-x^(n^j)) for n>1.

A196893 Number of partitions of 6^n into powers of n.

Original entry on oeis.org

1, 1, 284, 3987, 182832, 21719504, 6188114528, 3837284133564, 5498735029150412, 16177644099354374847, 104146398517005199125840, 1392276105682819242572329909, 37088099509347734659184844866868, 2148432835664289026090145748437694346

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..50

Row n=6 of A196879.

a(n) = [x^(6^n)] 1/Product_{j>=0}(1-x^(n^j)) for n>1.

A196894 Number of partitions of 7^n into powers of n.

Original entry on oeis.org

1, 1, 692, 18687, 1957192, 619319180, 527457882126, 1226373476385199, 6897556038713219072, 101539033269801820825743, 3421092256089716422594644400, 290708740669462708301488632766350, 55192415971099812757135585564036238784

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..50

Row n=7 of A196879.

a(n) = [x^(7^n)] 1/Product_{j>=0}(1-x^(n^j)) for n>1.

A196895 Number of partitions of 8^n into powers of n.

Original entry on oeis.org

1, 1, 1828, 82350, 18583582, 14357878818, 36521876237448, 270102925553717303, 6071277235712979102634, 365618223095981778848684187, 64402239847567589358641684368970, 28651633202605088497137960394142606995, 36379111301200246544606370148459181785142784

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..50

Row n=8 of A196879.

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

A196896 Number of partitions of 9^n into powers of n.

Original entry on oeis.org

1, 1, 4124, 342383, 154252476, 288862888125, 1952615455825446, 46188578538444709937, 3511244471110991227215296, 884267692532264259002637317099, 657656444358222872135019335879897500, 1581273532137910865654568892971737150590744

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..50

Row n=9 of A196879.

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

A196897 Number of partitions of 10^n into powers of n.

Original entry on oeis.org

1, 1, 9828, 1295579, 1166493640, 4963576426547, 86220169777616208, 5945914039134501155164, 1503179627327417142865920896, 1357042381209389119735863425487474, 4362395890943439751990308572939648140812, 45406477414358716832258194914969299144120147523

Offset: 0

Alois P. Heinz, Oct 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..50

Row n=10 of A196879.

a(n) = [x^(10^n)] 1/Product_{j>=0}(1-x^(n^j)) for n>1.

cp's OEIS Frontend

A196889 Number of partitions of 2^n into powers of n.

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A196890 Number of partitions of 3^n into powers of n.

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A196891 Number of partitions of 4^n into powers of n.

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A196892 Number of partitions of 5^n into powers of n.

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A196893 Number of partitions of 6^n into powers of n.

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A196894 Number of partitions of 7^n into powers of n.

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A196895 Number of partitions of 8^n into powers of n.

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A196896 Number of partitions of 9^n into powers of n.

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A196897 Number of partitions of 10^n into powers of n.

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