A078308 -id:A078308 - cp's OEIS frontend

A022742 Expansion of 1/Product_{m>=1} (1 - m*q^m)^18.

1, 18, 207, 1842, 13869, 92250, 557214, 3111624, 16272972, 80461694, 378917667, 1709416008, 7422200694, 31136646366, 126608628735, 500368588830, 1926482319873, 7240422289338, 26610335585263

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 18, g(n) = n. - Seiichi Manyama, Aug 16 2023

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

Column k=18 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (18/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

A022743 Expansion of 1/Product_{m>=1} (1 - m*q^m)^19.

Original entry on oeis.org

1, 19, 228, 2109, 16454, 113164, 705527, 4060870, 21863490, 111178196, 537978635, 2491812228, 11100464810, 47746888432, 198952868210, 805306011651, 3174012174213, 12206318615473, 45884592463642

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 19, g(n) = n. - Seiichi Manyama, Aug 16 2023

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

Column k=19 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (19/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

A022744 Expansion of 1/Product_{m>=1} (1 - m*q^m)^20.

Original entry on oeis.org

1, 20, 250, 2400, 19375, 137604, 884430, 5241000, 29017815, 151597440, 752997538, 3577442200, 16335561280, 71979549460, 307075300540, 1271938667704, 5127690095315, 20161295885120, 77454572685460

Offset: 0

N. J. A. Sloane

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 20, g(n) = n. - Seiichi Manyama, Aug 16 2023

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

Column k=20 of A297328.

Cf. A078308.

a(0) = 1; a(n) = (20/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023

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

Original entry on oeis.org

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

cp's OEIS Frontend

A022742 Expansion of 1/Product_{m>=1} (1 - m*q^m)^18.

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A022743 Expansion of 1/Product_{m>=1} (1 - m*q^m)^19.

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A022744 Expansion of 1/Product_{m>=1} (1 - m*q^m)^20.

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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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