A248871
Coefficients in asymptotic expansion of sequence A107895.
Original entry on oeis.org
1, 1, 3, 12, 66, 450, 3679, 35260, 388511, 4844584, 67502450, 1039929756, 17556193609, 322321551868, 6393505020803, 136245752898586, 3103879644045050, 75268872986970840, 1935571325829192247, 52605265683008056660, 1506530437404419817467
Offset: 0
A107895(n) / n! ~ 1 + 1/n + 3/n^2 + 12/n^3 + 66/n^4 + 450/n^5 + 3679/n^6 + ...
A256125
Coefficients in asymptotic expansion of sequence A077365.
Original entry on oeis.org
1, 1, 3, 12, 67, 457, 3734, 35741, 392875, 4886114, 67924417, 1044531625, 17609980356, 322993544751, 6402464186243, 136373115537072, 3105809328600351, 75300018326324541, 1936106590359322126, 52615058519875702993, 1506721174739412743551
Offset: 0
A077365(n) / n! ~ 1 + 1/n + 3/n^2 + 12/n^3 + 67/n^4 + 457/n^5 + 3734/n^6 + ...
A107894
Sum over the products of factorials of parts in all partitions of n where the sum runs over the number of different parts only.
Original entry on oeis.org
1, 1, 3, 9, 35, 167, 943, 6379, 48945, 429651, 4189865, 45307601, 535518109, 6883110373, 95435065935, 1420468921893, 22577620176887, 381695573051099, 6837601709298811, 129375694813679215, 2578070946813526485, 53964818587883937807, 1183805926540690127573
Offset: 0
The partitions of 5 are 1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2, 1+4, 2+3, 5, the corresponding products of factorials of parts are (when multiple parts are counted once only) 1!, 1!*2!, 1!*3!, 1!*2!, 1!*4!, 2!*3!, 5! and their sum is a(5) = 167.
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b:= proc(n, i) option remember;
`if`(n=0 or i<2, 1, b(n, i-1) +i!*add(b(n-i*j, i-1), j=1..n/i))
end:
a:= n-> b(n, n):
seq(a(n), n=0..30); # Alois P. Heinz, Apr 04 2012
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Total[Times@@@(Union/@IntegerPartitions[#]!)]&/@Range[20] (* Harvey P. Dale, Feb 26 2011 *)
b[n_, i_] := b[n, i] = If[n==0 || i<2, 1, b[n, i-1] + i!*Sum[b[n-i*j, i-1], {j, 1, n/i}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 29 2015, after Alois P. Heinz *)
A256126
Coefficients in asymptotic expansion of sequence A179327.
Original entry on oeis.org
1, 1, 3, 11, 50, 278, 1860, 14793, 138166, 1494034, 18422609, 255359957, 3929301362, 66412322717, 1222216175058, 24314268876147, 519701698551031, 11874016816562299, 288722141589331161, 7442890569982739838, 202733505298293899570, 5817564888930184685708
Offset: 0
A179327(n) / (n-1)! ~ 1 + 1/n + 3/n^2 + 11/n^3 + 50/n^4 + 278/n^5 + 1860/n^6 + ...
Showing 1-4 of 4 results.