A297328 -id:A297328 - cp's OEIS frontend

A022745 Expansion of 1/Product_{m>=1} (1 - m*q^m)^21.

1, 21, 273, 2716, 22659, 165984, 1098615, 6695559, 38085117, 204218630, 1040291595, 5064987207, 23686610269, 106828575357, 466231753944, 1974651627802, 8136148603086, 32681975601387, 128221943065839

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 21, g(n) = n. - Seiichi Manyama, Aug 16 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=21 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (21/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

A022746 Expansion of 1/Product_{m>=1} (1 - m*q^m)^22.

Original entry on oeis.org

1, 22, 297, 3058, 26334, 198748, 1353275, 8474202, 49475074, 272055454, 1420063656, 7079791314, 33881645721, 156287683310, 697257244178, 3017396237922, 12697675601127, 52071958360466, 208490926189117

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 22, g(n) = n. - Seiichi Manyama, Aug 16 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=22 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (22/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

A022747 Expansion of 1/Product_{m>=1} (1 - m*q^m)^23.

Original entry on oeis.org

1, 23, 322, 3427, 30429, 236371, 1654137, 10633291, 63665679, 358718373, 1917142690, 9779753341, 47860052964, 225631690224, 1028303816386, 4543788611823, 19515830222431, 81653870900161, 333437792190697

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 23, g(n) = n. - Seiichi Manyama, Aug 16 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=23 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (23/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

A022748 Expansion of 1/Product_{m>=1} (1 - m*q^m)^24.

Original entry on oeis.org

1, 24, 348, 3824, 34974, 279360, 2007496, 13236528, 81211749, 468506720, 2561834052, 13362262272, 66823739654, 321763781664, 1497035306088, 6750151072304, 29572851319506, 126163172338056, 525134328872668

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 24, g(n) = n. - Seiichi Manyama, Dec 29 2017

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=24 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (24/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

A022749 Expansion of 1/Product_{m>=1} (1 - m*q^m)^25.

Original entry on oeis.org

1, 25, 375, 4250, 40000, 328255, 2420250, 16355625, 102754175, 606511425, 3390891675, 18072320050, 92298482475, 453641400625, 2153379245600, 9902221659300, 44225723552250, 192274295402250

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 25, g(n) = n. - Seiichi Manyama, Aug 17 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=25 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (25/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

A022750 Expansion of 1/Product_{m>=1} (1 - m*q^m)^26.

Original entry on oeis.org

1, 26, 403, 4706, 45539, 383630, 2899936, 20071012, 129029953, 778729224, 4448625272, 24212010550, 126207077867, 632795395052, 3062954205181, 14356406110410, 65330892459924, 289297563109646

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 26, g(n) = n. - Seiichi Manyama, Aug 17 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=26 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (26/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

A022751 Expansion of 1/Product_{m>=1} (1 - m*q^m)^27.

Original entry on oeis.org

1, 27, 432, 5193, 51624, 446094, 3454767, 24472584, 160883037, 992189253, 5788156617, 32151489435, 170956128834, 873959259258, 4311311541669, 20586621297483, 95404964600448, 430094901683700

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 27, g(n) = n. - Seiichi Manyama, Aug 17 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=27 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (27/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

A022752 Expansion of 1/Product_{m>=1} (1 - m*q^m)^28.

Original entry on oeis.org

1, 28, 462, 5712, 58289, 516292, 4093670, 29660488, 199276056, 1255092972, 7472840004, 42341686632, 229538522801, 1195827758664, 6009154128786, 29217982425632, 137830326653131, 632273980209340

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 28, g(n) = n. - Seiichi Manyama, Aug 17 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=28 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (28/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

A022753 Expansion of 1/Product_{m>=1} (1 - m*q^m)^29.

Original entry on oeis.org

1, 29, 493, 6264, 65569, 594906, 4826325, 35745951, 245302938, 1576968409, 9577863060, 55328931365, 305653898806, 1621966962395, 8298721485505, 41068822192297, 197116507655270, 919734407613752

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 29, g(n) = n. - Seiichi Manyama, Aug 17 2023

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Column k=29 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (29/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

A022754 Expansion of 1/Product_{m>=1} (1 - m*q^m)^30.

Original entry on oeis.org

1, 30, 525, 6850, 73500, 682656, 5663205, 42852150, 300202485, 1968839760, 12192045213, 71771729100, 403849667345, 2181900748410, 11361561151605, 57202802787016, 279230335572240, 1324656422161470

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 30, g(n) = n. - Seiichi Manyama, Aug 17 2023

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Column k=30 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (30/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 17 2023

cp's OEIS Frontend

A022745 Expansion of 1/Product_{m>=1} (1 - m*q^m)^21.

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A022746 Expansion of 1/Product_{m>=1} (1 - m*q^m)^22.

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A022747 Expansion of 1/Product_{m>=1} (1 - m*q^m)^23.

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A022748 Expansion of 1/Product_{m>=1} (1 - m*q^m)^24.

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A022749 Expansion of 1/Product_{m>=1} (1 - m*q^m)^25.

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A022750 Expansion of 1/Product_{m>=1} (1 - m*q^m)^26.

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A022751 Expansion of 1/Product_{m>=1} (1 - m*q^m)^27.

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A022752 Expansion of 1/Product_{m>=1} (1 - m*q^m)^28.

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A022753 Expansion of 1/Product_{m>=1} (1 - m*q^m)^29.

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A022754 Expansion of 1/Product_{m>=1} (1 - m*q^m)^30.

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