A032300 -id:A032300 - cp's OEIS frontend

A371310 Expansion of e.g.f. Product_{k>=1} (1 + prime(k)*x^k/k!).

1, 2, 3, 23, 47, 231, 2260, 6527, 35151, 224759, 3434124, 12476055, 79758206, 491191521, 4752819625, 105146082344, 393097093065, 2976053272527, 21569670506914, 188844207315245, 2277243901499454, 72603521472295945, 326137558352646889, 2491611720654851668

Offset: 0

Ilya Gutkovskiy, Mar 24 2024

nonn

"EFJ" (unordered, size, labeled) transform of primes.

C. G. Bower, Transforms (2)

Cf. A000040, A007837, A032299 A032300, A147655.

nmax = 23; CoefficientList[Series[Product[(1 + Prime[k] x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

A371311 Expansion of e.g.f. Product_{k>=1} (1 + k*x^k/(k-1)!).

Original entry on oeis.org

1, 1, 4, 21, 52, 465, 3306, 14161, 74208, 960777, 10558630, 44851521, 361716576, 2473446157, 46951741760, 735722365995, 3502764883456, 27660533205537, 257573937401838, 2415069153393553, 62591287234200960, 1356650271603527061, 6966660193683272104, 61046400429116180475

Offset: 0

Ilya Gutkovskiy, Mar 24 2024

nonn

"EFJ" (unordered, size, labeled) transform of squares.

C. G. Bower, Transforms (2)

Cf. A000290, A007837, A032299, A032300, A092484.

nmax = 23; CoefficientList[Series[Product[(1 + k x^k/(k - 1)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

cp's OEIS Frontend

A371310 Expansion of e.g.f. Product_{k>=1} (1 + prime(k)*x^k/k!).

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