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 A133991 a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2^k+n-1,n). 1
 1, 3, 17, 193, 5427, 463023, 134675759, 139917028089, 527871326293913, 7281357469833220843, 368715613115281663650597, 68787958348542935934247206953, 47453320297069210448891035137347047 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = (1/n!)*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)*(2^k+1)^n. G.f.: Sum_{n>=0} (-log(1 - (2^n+1)*x))^n/n!. a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jun 08 2019 MATHEMATICA Table[Sum[(-1)^(n-k) * StirlingS1[n, k]*(2^k + 1)^n, {k, 0, n}]/n!, {n, 0, 12}] (* Vaclav Kotesovec, Jun 08 2019 *) CROSSREFS Sequence in context: A158885 A202424 A335343 * A210898 A009494 A267659 Adjacent sequences:  A133988 A133989 A133990 * A133992 A133993 A133994 KEYWORD easy,nonn AUTHOR _Paul Hanna_ and Vladeta Jovovic, Jan 21 2008 EXTENSIONS More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008 STATUS approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)