A383206 -id:A383206 - cp's OEIS frontend

A383207 Expansion of e.g.f. (exp(f(x)) - 1)^2 / 2, where f(x) = (exp(2*x) - 1)/2.

0, 0, 1, 9, 71, 575, 4957, 45829, 454015, 4804191, 54094749, 645720757, 8142419727, 108110708511, 1506969153757, 21993472779461, 335257957315199, 5325979566073919, 87999598425114045, 1509471498829147637, 26835040585117438415, 493677094649876461759, 9384926300821643459133

Offset: 0

Seiichi Manyama, Apr 19 2025

nonn

Column k=2 of A383206.

Cf. A000558.

a(n) = sum(k=2, n, 2^(n-k)*stirling(n, k, 2)*stirling(k, 2, 2));

a(n) = Sum_{k=2..n} 2^(n-k) * Stirling2(n,k) * Stirling2(k,2).

A383208 Expansion of e.g.f. (exp(f(x)) - 1)^3 / 6, where f(x) = (exp(2*x) - 1)/2.

Original entry on oeis.org

0, 0, 0, 1, 18, 245, 3120, 39697, 517790, 6999785, 98520060, 1445923149, 22129416210, 352932509085, 5859167661256, 101122879922313, 1811960841148774, 33662625853200337, 647550189266734452, 12881675626292023173, 264677402162135670554, 5610552395871699336453

Offset: 0

Seiichi Manyama, Apr 19 2025

nonn

Column k=3 of A383206.

Cf. A000559.

a(n) = sum(k=3, n, 2^(n-k)*stirling(n, k, 2)*stirling(k, 3, 2));

a(n) = Sum_{k=3..n} 2^(n-k) * Stirling2(n,k) * Stirling2(k,3).

cp's OEIS Frontend

A383207 Expansion of e.g.f. (exp(f(x)) - 1)^2 / 2, where f(x) = (exp(2*x) - 1)/2.

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