A308371 -id:A308371 - cp's OEIS frontend

A308369 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} 1/(1 - A(x^k))^k.

1, 1, 4, 12, 41, 133, 485, 1752, 6677, 25809, 102130, 409532, 1665128, 6837348, 28333334, 118288386, 497120101, 2101181482, 8926401690, 38093403136, 163224292328, 701951448268, 3028792691947, 13108224143298, 56887750453404, 247512117880754, 1079421026637431

Offset: 1

Ilya Gutkovskiy, May 22 2019

nonn

Cf. A050383, A091865, A308370, A308371, A308372.

terms = 27; A[] = 0; Do[A[x] = x Product[1/(1 - A[x^k])^k, {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

G.f. A(x) satisfies: A(x) = x * exp(Sum_{k>=1} Sum_{d|k} d^2 * A(x^d)^(k/d) / k).

A308370 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + A(x^k))^k.

Original entry on oeis.org

1, 1, 3, 8, 20, 47, 118, 280, 681, 1640, 3963, 9523, 23004, 55377, 133477, 321597, 775054, 1867304, 4499934, 10842847, 26127768, 62958232, 151708512, 365562567, 880881465, 2122617010, 5114772619, 12324827128, 29698572295, 71563264162, 172442689864, 415527172616

Offset: 1

Ilya Gutkovskiy, May 22 2019

nonn

Cf. A050383, A091865, A308369, A308371, A308372.

terms = 32; A[] = 0; Do[A[x] = x Product[(1 + A[x^k])^k, {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

G.f. A(x) satisfies: A(x) = x * exp(-Sum_{k>=1} Sum_{d|k} d^2 * (-A(x^d))^(k/d) / k).

A308372 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + k*A(x^k)).

Original entry on oeis.org

1, 1, 3, 8, 19, 45, 110, 259, 614, 1466, 3479, 8239, 19581, 46445, 110209, 261555, 620649, 1472597, 3494663, 8292514, 19677729, 46694303, 110804310, 262932172, 623928374, 1480555791, 3513297447, 8336903884, 19783134767, 46944538382, 111397439864, 264341463510

Offset: 1

Ilya Gutkovskiy, May 22 2019

nonn

Cf. A050383, A091865, A308369, A308370, A308371.

terms = 32; A[] = 0; Do[A[x] = x Product[(1 + k A[x^k]), {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest

G.f. A(x) satisfies: A(x) = x * exp(-Sum_{k>=1} Sum_{d|k} d * (-d * A(x^d))^(k/d) / k).

cp's OEIS Frontend

A308369 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} 1/(1 - A(x^k))^k.

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A308370 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + A(x^k))^k.

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Author

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Crossrefs

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Mathematica

Formula

A308372 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + k*A(x^k)).

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Keywords

Crossrefs

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Mathematica

Formula