A353893
Expansion of e.g.f. exp( (x * log(1-x))^4 / 576 ).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 17850, 242550, 3350655, 48108060, 724403680, 11478967500, 191601229820, 3367499575440, 62253354650760, 1208755315895400, 24611454394536780, 524613603866302440, 11687734234226039220, 271715852337632107020
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*log(1-x))^4/576)))
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a(n) = n!*sum(k=0, n\8, (4*k)!*abs(stirling(n-4*k, 4*k, 1))/(576^k*k!*(n-4*k)!));
A353894
Expansion of e.g.f. exp( (x * (exp(x) - 1))^2 / 4 ).
Original entry on oeis.org
1, 0, 0, 0, 6, 30, 105, 315, 2128, 24948, 251415, 2093025, 16437036, 148728294, 1693067467, 21459867975, 270217289280, 3338860150488, 42428729660751, 581966068060485, 8654787480759700, 135253842794286930, 2163416823356628147, 35313421249845594075
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^2/4)))
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a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*k!*(n-2*k)!));
A353895
Expansion of e.g.f. exp( (x * (exp(x) - 1))^3 / 36 ).
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 20, 210, 1400, 7560, 36120, 159390, 850300, 9875580, 170133964, 2688015330, 36706233200, 444802722000, 4939264076016, 52543545234534, 583037908936500, 7645631225897700, 124931080233222340, 2327407301807577066, 44282377224446369800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^3/36)))
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a(n) = n!*sum(k=0, n\6, (3*k)!*stirling(n-3*k, 3*k, 2)/(36^k*k!*(n-3*k)!));
Showing 1-3 of 3 results.